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Date Posted: 14:17:13 07/29/17 Sat

Where do you think you would spend eternity, if God forbid, you were to die later today?

I am not sending this to you to preach religion. I am asking you if you were standing before a Holy God do you think that He would have an issue with your sin if you were standing in front of a Holy God?

Because that is exactly what the Bible tells us. That a Holy God can not be in the presence of sin. So every human being that has ever lived has had the exact same problem. This sin problem. But do you also know that Jesus Christ offers all of us a free gift, the forgiveness of sin. And faith and belief is all God wants from you. So, do you believe that Jesus was the Son of God who came to earth and lived a perfect life? Do you know that God will accept Christ's perfect life and let Christ be your Advocate, so on Judgement Day God doesn't look at all the bad stuff you've done. Instead, God will look at His perfect Son when He see's you. Because Jesus and His perfection literally stand in our place.

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[> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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[ Post a Reply to This Message ]
[> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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Date Posted: 12:59:48 09/09/14 Tue

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[ Post a Reply to This Message ]
[> [> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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[ Post a Reply to This Message ]
[> [> [> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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[ Post a Reply to This Message ]
[> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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Date Posted: 20:08:31 12/14/14 Sun

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[ Post a Reply to This Message ]
[> Subject: Re: Magix Movie Edit Pro 17 Plus Crack Serial Keygen Cd Key.rar


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Subject: coordinate geometry: linear equations in two variables


Author:
Misty Bowman
[ Edit | View ]

Date Posted: 18:06:25 06/18/05 Sat

what is the equation of the line that contains the points with (x,y)coordinates(-3,7) and (5,-1)? I need to know how to do this problem step by step.

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
QUITTNER
[ Edit | View ]

Date Posted: 07:17:31 06/20/05 Mon

>>> what is the equation of the line that contains the points with (x,y)coordinates(-3,7) and (5,-1)? <<<
..... The equation of a straight line is y=ax+b. Just insert the given values into the two simultaneous equations, and solve them for a and for b.
7=(-3)a + b
(-1)= 5a + b

[ Post a Reply to This Message ]
[> [> Subject: Re: coordinate geometry: linear equations in two variables


Author:
kanishkporwal
[ Edit | View ]

Date Posted: 00:44:59 09/15/11 Thu

>>>> what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? <<<
>..... The equation of a straight line is y=ax+b. Just
>insert the given values into the two simultaneous
>equations, and solve them for a and for b.
> 7=(-3)a + b
>(-1)= 5a + b
now you just need to solve these two linear equations
for solving linear equations you just need to
subtract eq 2 from eq 1 to get
8=(-8)a
a=-1
put a in any of the two equations to find b

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
fizixx
[ Edit | View ]

Date Posted: 18:01:22 12/01/05 Thu

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.

The equation of a line is:

y = mx + b

m is the slope
x is the independent variable
b is the 'y' intercept
y is the dependent variable

You essentially have to supply 'm' and 'b'.

You can use the following formula:

y - y1 = mx - x1

This is the pont-slope equation, and you have all this information at hand.

m = (y2 - y1)/(x2 - x1)

Let

y1 = -3
y2 = 5
x1 = 7
x2 = -1

It really doesn't matter which ones you pick, as long as the x values correspond to the actual x coordinate given....same for y.. in other words. If you have (8,5)....x = 8 and y = 5. You can't switch this. Understand?

So, plug this in and you will find that m = -8/8 = -1

Then the point-slope equation becomes:

y - 7 = -x - (-3)
==> y - 7 = -x + 3
==> y = -x + 3 + 7
==> y = -x + 10

That's your equation. Hope this makes sense.

fizixx

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
Yvette Jones
[ Edit | View ]

Date Posted: 16:09:10 01/24/11 Mon

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
nicole heath
[ Edit | View ]

Date Posted: 13:25:41 03/07/11 Mon

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
Amber
[ Edit | View ]

Date Posted: 16:45:05 04/27/11 Wed

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.
THE ABOVE ANSWER IS INCORRECT!!! The answer is y=-X+4
PLEASE EXPLAIN HOW!!!! THANKS!

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
Jamaine
[ Edit | View ]

Date Posted: 00:43:22 10/27/11 Thu

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.


Well we start by knowing that the equation for finding the slope is m=(y1-y2)
-------
(x1-x2)

Just plug your coordinate's in :
you should get the answer -1

Then go back to slope form which is y=mx+b, insert one set of your coordinates along with your slope and solve for b.

for example 7=(-1)(-3) + b
7= 3 + b
-4=b
put this back in its form you have y=-x-4

hope this helps, and Im not a teacher so it might be explained a litte hood.

[ Post a Reply to This Message ]
[> [> Subject: Re: coordinate geometry: linear equations in two variables


Author:
geeknick (Mathy..!!!!)
[ Edit | View ]

Date Posted: 23:21:52 12/15/11 Thu

Linear equations (slope) help?
I am just not getting this. If you could help me that would be wonderful! Thank you!


1. The pitch of a roof is just the slope of the roof. Of course in the real world, we dont have an xyplane, so we only use positive (or at least non-negative) slopes.
(a) If a roof has a pitch of zero what does it look like?
(b) If the pitch of the roof is a very large number, what does the roof look like?
(c) Suppose your roof is 27 feet above the ground at its peak and only 22 feet above the ground at
the front of the house. How far does it rise?
(d) Suppose the front of the house is 17 feet from the street and the peak is 32 feet from the street
(measure just horizontally). How far is the run from the front edge to the peak?
(e) What is the pitch of this roof?
(f) Why do we care about the pitch of the roof? For what reasons could a steeper roof be better
and for what reasons would a less steep roof be better?
2. The grade of a road is just the slope converted into a percent. So when you find the slope, multiply
by 100 to get the grade. Again we use only non-negative slopes.
(a) A road rises 12 feet over a horizontal distance of 640 feet.
What is its slope?
What is its grade?
(b) A road has a 16.7% grade.
What is its slope?

[ Post a Reply to This Message ]
[> [> Subject: Re: coordinate geometry: linear equations in two variables


Author:
Davida
[ Edit | View ]

Date Posted: 23:34:16 07/31/12 Tue

>>what is the equation of the line that contains the
>>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>>to know how to do this problem step by step.
>
>
>Well we start by knowing that the equation for finding
>the slope is m=(y1-y2)
> -------
> (x1-x2)
>
>Just plug your coordinate's in :
>you should get the answer -1
>
>Then go back to slope form which is y=mx+b, insert one
>set of your coordinates along with your slope and
>solve for b.
>
>for example 7=(-1)(-3) + b
> 7= 3 + b
> 4=b
>put this back in its form you have y=-x+4
>
>hope this helps, and Im not a teacher so it might be
>explained a litte hood.

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
erica
[ Edit | View ]

Date Posted: 15:18:37 11/01/11 Tue

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
NICK (http://calculator.tutorvista.com)
[ Edit | View ]

Date Posted: 00:22:07 11/03/11 Thu

Steps for Calculating Compound Interest
Step 1 :

Formula for calculating the total amount,

Total amount = P(1+(R/100))n.

Compound interest = Total amount - principal.


Step 2 :

When the Time is given in months then:

1 month= 0.08, 2 months = 0.17, 3 months= 0.25, 4 months= 0.33, 5 months= 0.42, 6 months= 0.50, 7 months= 0.58, 8 months= 0.67, 9 months= 0.75, 10 months= 0.83 and 11 months= 0.92.

http://calculator.tutorvista.com/math/33/compound-interest-calculator.html

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
Engr. Lawrence peter
[ Edit | View ]

Date Posted: 09:38:03 09/08/12 Sat

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.
solution
lets assume that (-3,7) is coordinate 1 i.e x1 is -3 y1 is 7 and (5,-1) is coordinate 2 i.e x2 is 5 and y2 is -1
using d formula
y-y1/x-x1=y2-y1/x2-x1
by putting in the values of the coordinate u get
y-7/x-(-3)= -1-7/5-(-3)
y-7/x+3 =-8/5+3
y-7/x+3= -8/8
y-7/x+3=-1/1
by cross multiplying you get
1(y-7)=-1(x+3)
open the brackets you get
y-7=-x-3
collect like terms you get
y+x=7-3
y+x=4
this is your required equatn thank you hope I helped

[ Post a Reply to This Message ]
[> [> Subject: Re: coordinate geometry: linear equations in two variables


Author:
MK (Thankful)
[ Edit | View ]

Date Posted: 13:49:40 08/19/15 Wed

>>what is the equation of the line that contains the
>>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>>to know how to do this problem step by step.
> solution
>lets assume that (-3,7) is coordinate 1 i.e x1 is -3
>y1 is 7 and (5,-1) is coordinate 2 i.e x2 is 5 and y2
>is -1
>using d formula
> y-y1/x-x1=y2-y1/x2-x1
>by putting in the values of the coordinate u get
>y-7/x-(-3)= -1-7/5-(-3)
>y-7/x+3 =-8/5+3
>y-7/x+3= -8/8
>y-7/x+3=-1/1
>by cross multiplying you get
>1(y-7)=-1(x+3)
>open the brackets you get
>y-7=-x-3
>collect like terms you get
>y+x=7-3
>y+x=4
>this is your required equatn thank you hope I helped



It definitely helped, sir. THANKS ALOT!

[ Post a Reply to This Message ]
[> Subject: Re: coordinate geometry: linear equations in two variables


Author:
kimberley
[ Edit | View ]

Date Posted: 14:17:45 02/09/13 Sat

>what is the equation of the line that contains the
>points with (x,y)coordinates(-3,7) and (5,-1)? I need
>to know how to do this problem step by step.esaiser version

[ Post a Reply to This Message ]
Subject: Is anybody there/here?


Author:
QUITTNER
[ Edit | View ]

Date Posted: 13:04:49 11/12/14 Wed

Maybe nobody needs mathematical help? Keep well, good health is more valuable than money!

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Subject: Finding equation of a parabola with the use of 3 points


Author:
Joanna
[ Edit | View ]

Date Posted: 23:51:55 05/11/03 Sun

I'm doing some tutorial questions on matrices and one asked you to find the equation of a parabola that passes thru' 3 points....(3,-1), (1,-7) and (-2,14). I was wondering if anyone knows what processes/formula i should use to find the answer? Thanx.

[ Post a Reply to This Message ]
[> Subject: Re: Finding equation of a parabola with the use of 3 points


Author:
QUITTNER
[ Edit | View ]

Date Posted: 06:21:51 05/23/03 Fri

Joanna, I assume that you know how to invert a matrix. One of he equations of a parabola is A+Bx+Cx^2=y, which can also be written as Ax^0+Bx^1+Cx^2=y, where x^0 is always 1. A Polynomial of nth degree needs n+1 points; here we have a 2nd degree polynomial and 3 points, that's OK.
..... Let matrix M1 equal the left side of the equation, and fill in all the x's as follows:
Take one of the points (in any order), (3,-1) first. Its x is 3, therefore the top line of M1 is 1, for x'0, 3 for x, and 9 for x'2. The 2nd line is for point (1,-7): 1,1,1. The 3rd line for point (-2,14) is 1,-2,4. Therefore, to repeat, M1 is

| 1 3 9 | for point 1,
| 1 1 1 } 2,
| 1 =2 4 | 3.

The right side of the equation of the parabola is only y, we then make Matrix M2 equal to
| -1 | for point 1,
| -7 | 2,
| 14 | 3.

Next invert M1 to get matrix M3:
| 1/5 1 1/5 |
| 1/10 1/6 -15/4 |
| 1/10 -1/6 1/15 |

To get the results matrix, multiply M2 by M3, giving
| -4 |
| -5 |
| 2 | Therefore the equation of the parabola is
A+Bx+Cx^2=y where A=-4, B=-5 and C=2. Make sure you check this by evaluating the equation for each of the given x values of each of the 3 points and see that you get the given y's.

[ Post a Reply to This Message ]
[> [> Subject: Finding equation of a parabola with vertex at Oy and passing thru (2,2)


Author:
lanie
[ Edit | View ]

Date Posted: 18:00:29 11/06/03 Thu

>Joanna, I assume that you know how to invert a matrix.
>One of he equations of a parabola is A+Bx+Cx^2=y,
>which can also be written as Ax^0+Bx^1+Cx^2=y, where
>x^0 is always 1. A Polynomial of nth degree needs n+1
>points; here we have a 2nd degree polynomial and 3
>points, that's OK.
>..... Let matrix M1 equal the left side of the
>equation, and fill in all the x's as follows:
>Take one of the points (in any order), (3,-1) first.
>Its x is 3, therefore the top line of M1 is 1, for
>x'0, 3 for x, and 9 for x'2. The 2nd line is for point
>(1,-7): 1,1,1. The 3rd line for point (-2,14) is
>1,-2,4. Therefore, to repeat, M1 is
>
>| 1 3 9 | for point 1,
>| 1 1 1 } 2,
>| 1 =2 4 | 3.
>
>The right side of the equation of the parabola is only
>y, we then make Matrix M2 equal to
>| -1 | for point 1,
>| -7 | 2,
>| 14 | 3.
>
>Next invert M1 to get matrix M3:
>| 1/5 1 1/5 |
>| 1/10 1/6 -15/4 |
>| 1/10 -1/6 1/15 |
>
>To get the results matrix, multiply M2 by M3, giving
>| -4 |
>| -5 |
>| 2 | Therefore the equation of the parabola is
>A+Bx+Cx^2=y where A=-4, B=-5 and C=2. Make sure
>you check this by evaluating the equation for each of
>the given x values of each of the 3 points and see
>that you get the given y's.

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding equation of a parabola with vertex at Oy and passing thru (2,2)


Author:
QUITTNER
[ Edit | View ]

Date Posted: 11:19:31 11/11/03 Tue

You wrote: "Finding equation of a parabola with vertex at Oy and passing thru (2,2)"
..... I suppose this means that the vertex is at the ORIGIN (0,0), and that one point is at (2,2)
..... We have the general equation y-k=a(x-h)^2 where, in our case k and h are both zero. Therefore
y=a*x^2 and in our case 2=a*2^2=4a. Therefore a=1/2 and
y=(1/2)*x^2
..... Check it out: if x=2 then y=1/2 of 4, y=2 OK

[ Post a Reply to This Message ]
[> Subject: Finding equation of a parabola


Author:
Maria
[ Edit | View ]

Date Posted: 23:03:22 04/24/04 Sat

hi, could you please tell me how to find the equation of a line (not a straightline), with points (8,11) and the other one is (x,35) where x is an unknown coordinate. the slope is 0. This is a parabola. Thank you very much.

[ Post a Reply to This Message ]
[> [> Subject: Re: Finding equation of a parabola


Author:
QUITTNER
[ Edit | View ]

Date Posted: 12:57:38 04/26/04 Mon

>hi, could you please tell me how to find the equation
>of a line (not a straightline), with points (8,11) and
>the other one is (x,35) where x is an unknown
>coordinate. the slope is 0. This is a parabola. Thank
>you very much.
..... A parabola has very many points, and there is a slope at every one of them. You say the slope is 0, but you don't say at which point that slope is zero.

[ Post a Reply to This Message ]
[> Subject: Re: Finding equation of a parabola with the use of 3 points


Author:
Mpho
[ Edit | View ]

Date Posted: 07:50:56 08/16/13 Fri

>I'm doing some tutorial questions on matrices and one
>asked you to find the equation of a parabola that
>passes thru' 3 points....(3,-1), (1,-7) and (-2,14). I
>was wondering if anyone knows what processes/formula i
>should use to find the answer? Thanx.

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Subject: Finding the Equation of a Parabola using the vertex and 1 point


Author:
Ed
[ Edit | View ]

Date Posted: 22:13:15 11/05/03 Wed

I seem to not be able to come up with the right answers for the following problem:

vertex (5,12), Point (7,15)
I know that standard form is f(x)=a(x-h)^2+k
how do i plug these in to get the proper answer.
The book gives the answer as -3/4(x-5)^2+12

How do I get to that answer?

[ Post a Reply to This Message ]
[> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
QUITTNER
[ Edit | View ]

Date Posted: 09:11:49 11/10/03 Mon

>vertex (5,12), Point (7,15)
>I know that standard form is f(x)=a(x-h)^2+k
>how do i plug these in to get the proper answer.
>The book gives the answer as -3/4(x-5)^2+12
..... We have two points (x,y), with the vertex being one of them. We also know that
y=a(x-h)^2+k This is (y-k)=a*(x-h)^2
Note that we deal here with the differences in x and in y, distances from the (given) vertex. Therefore k=the y of the vertex, and h is the x of the vertex.
Therefore (15-12)=a*(7-5)^2
3=a*(2)^2 and 3=a*4 giving a=3/4
The parabola's equation is therefore for ANY x and y:
y=(3/4)*(x-5)^2 + 12 COMPARE with the book's answer.

[ Post a Reply to This Message ]
[> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
masnah binti abd.rahim
[ Edit | View ]

Date Posted: 02:59:18 09/09/04 Thu

>>vertex (5,12), Point (7,15)
>>I know that standard form is f(x)=a(x-h)^2+k
>>how do i plug these in to get the proper answer.
>>The book gives the answer as -3/4(x-5)^2+12
>..... We have two points (x,y), with the vertex being
>one of them. We also know that
>y=a(x-h)^2+k This is (y-k)=a*(x-h)^2
>Note that we deal here with the differences in x and
>in y, distances from the (given) vertex. Therefore
>k=the y of the vertex, and h is the x of the vertex.
>Therefore (15-12)=a*(7-5)^2
>3=a*(2)^2 and 3=a*4 giving a=3/4
>The parabola's equation is therefore for ANY x and y:
>y=(3/4)*(x-5)^2 + 12 COMPARE with the book's answer.

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
QUITTNER
[ Edit | View ]

Date Posted: 10:17:49 09/09/04 Thu

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[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola


Author:
Justin
[ Edit | View ]

Date Posted: 15:55:44 02/21/05 Mon

if the problem says express each equation in the form y=a(x-h)+k or x=a(y-k)+h, then how do you do y=2x-12x+6?

[ Post a Reply to This Message ]
[> [> [> [> Subject: Re: Finding the Equation of a Parabola


Author:
QUITTNER
[ Edit | View ]

Date Posted: 10:00:46 02/22/05 Tue

>>> if the problem says express each equation in the form y=a(x-h)+k or x=a(y-k)+h, then how do you do y=2x-12x+6?
..... First you selcet the proper equation. Here the left side is y, therefore use y=a(x-h)^2+k. Expand this to get
y=a*(x^2-2hx+h^2) + k or
y=a(x^2) - 2ahx +a(h^2) + k (1) We also know
y=2x^2) - 12x + 6 (2)
Compare the coeficients of equation (1) with those of (2):
a=2 4h=12, h=3 18+k=6, k=-12

Always check your answers:
y=2*(x-3)^2 - 12 = 2*(x^2-6x+9) - 12 =
y=2*(x^2)-12x+18-12 OK

[ Post a Reply to This Message ]
[> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
Kristen
[ Edit | View ]

Date Posted: 09:33:14 10/18/04 Mon

y=a(h-h)* +k (*=^2)
fill in your points
15=a(7-5)*+12
15-12=a(2)*
3=4a
a=3/4

Standard, fill in a and vertex
a(x-h)*+k
3/4(x-5)*+12

thus that is your equation in standard form

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
Kristen
[ Edit | View ]

Date Posted: 09:34:19 10/18/04 Mon

>y=a(h-h)* +k (*=^2)
>fill in your points
>15=a(7-5)*+12
>15-12=a(2)*
>3=4a
>a=3/4
>
>Standard, fill in a and vertex
>a(x-h)*+k
>3/4(x-5)*+12
>
>thus that is your equation in standard form

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
QUITTNER
[ Edit | View ]

Date Posted: 07:49:56 10/19/04 Tue

Given that the vertex has coordinates (a,b), and the one give point has coordinats (x1,y1)
Starting with the equation of a parabola:
(y-a)^2 = k * (x-b)
We know a and b (the vertex), and we can then use
(y1-a)^2 = k * (x1-b) to find k

[ Post a Reply to This Message ]
[> [> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
QUITTNER
[ Edit | View ]

Date Posted: 08:05:59 10/19/04 Tue

CORRECTION: (Reversing a and b in my previous post):

Given that the vertex has coordinates (a,b), and the
one given point has coordinates (x1,y1)

Starting with the equation of a parabola:
(y-b)^2 = k * (x-a)
We know a and b (the vertex), and we can then use
(y1-b)^2 = k * (x1-a) to find k

[ Post a Reply to This Message ]
[> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
leslie ann peji
[ Edit | View ]

Date Posted: 03:48:04 08/16/10 Mon

the x and y coordinates of the vertex gives the values of h and k respectively
hence, h=5 and k=12

the equation can be written as y=a(x-5)^2+12 "a" can be found using the fact that the point (7, 15)is on the graph of the line. 15= a(7-5)^2+12
15=4a+12
4a=15-12
a=-3/4
therefore, y=a(x-h)^2+12

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
leslie ann peji
[ Edit | View ]

Date Posted: 03:54:36 08/16/10 Mon

>the x and y coordinates of the vertex gives the values
>of h and k respectively
> hence, h=5 and k=12
>
>the equation can be written as y=a(x-5)^2+12 "a" can
>be found using the fact that the point (7, 15)is on
>the graph of the line. 15= a(7-5)^2+12
> 15=4a+12
> 4a=15-12
> a=-3/4
> therefore, y=a(x-h)^2+12 answer: y=-3/4(x-5)^2+12

[ Post a Reply to This Message ]
[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
simon (sad)
[ Edit | View ]

Date Posted: 05:56:35 03/23/13 Sat

I am finding it hard to find the equation of the parabola given the vertex(7,-2) and a x-intercept(4,0). How will i get or find the equation of the parabola.

[ Post a Reply to This Message ]
[> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point


Author:
sarah
[ Edit | View ]

Date Posted: 09:31:26 02/13/13 Wed

Find the standard equation of the parabola that has a vertical axis that has x-intercept -5 and 3 has a lowest point with a y-coordinate of -7

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Subject: Hints for mathematical Topic wanted, Solution heavenly!


Author:
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[ Edit | View ]

Date Posted: 06:14:20 09/05/03 Fri

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I got a numerical solution for the equations.

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[> Subject: please help me!


Author:
Rawan Kilo
[ Edit | View ]

Date Posted: 18:47:48 02/09/04 Mon

The volume of the rectangular solid is given by the expression 34.944x(cubed)+44.684x(squared)-8.29x-16.8. The surface area of one side of the rectangular solid is given by the expression 6.72x(squared)+12.47+5.6. The sum of the dimensions of the rectangular solid to the nearest hundredth.
You must utilize handheld technology to answer the problem and provide sketches of the graphs representing the cubic and quadratic expressions seen on handheld screen to justify your explanations.

[ Post a Reply to This Message ]
[> [> Subject: Re: please help me!


Author:
QUITTNER
[ Edit | View ]

Date Posted: 12:31:45 02/13/04 Fri

>The volume of the rectangular solid is given by the
>expression 34.944x(cubed)+44.684x(squared)-8.29x-16.8.
>The surface area of one side of the rectangular solid
>is given by the expression 6.72x(squared)+12.47+5.6.
>The sum of the dimensions of the rectangular solid to
>the nearest hundredth.
..... What is the difficulty? You are given a volume of a rectangular solid in terms of an equation, call it y3 (3-dimensional).
..... You are also given the surface area of one side in terms of an equation, call it y2 (2-dimensional).
..... The volume of a rectangular solid is one side's length times the surface area of one side, so that y3 divided by y2 should give you the equation of the side's length, call it y1 (1-dimensional).
..... The graphs of these equations are partly negative, so you must first mention, then reject the negative parts. y1 appears to be sufficiently linear (depends on how many decimal places are used in the calculations), so that any two points can be used to get the equation of that line, such as the (approximate) root of y1 and its (-ve) intercept on the y-axis. Can you take it from here?

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[> [> [> Subject: Re: please help me!


Author:
geeknick (sad)
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Date Posted: 23:59:29 11/04/11 Fri

1/1+a^n + 1/1+a^-n
My attempt:=1/1+a^n + 1+a^n/1=1+{1+a^n(1+a^n)}/1+a^n=1+1+2a^n+a^n^2/1+a^n=2+2a^n+a^n^2/1+a^nlet a^n=m=2+2m+2m^2/1+m=2(1+m+m^2)/1+m
I don't know what to do next, the answer is supposed to be 1.

will you please simplify the expression its very urgent... i tried on Many forum sites but didn't get the correct answer according to my mathematics textbook.


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Subject: Math Problem (easy, but I don't know)


Author:
Joe Francis
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Date Posted: 19:46:17 11/18/02 Mon

A rectangle lot 30m by 20m is surrounded on all four sides by a concrete walk 3m wide. If you need to concrete only the sidewalk, how much concrete will you need? (surface area)

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[> Subject: Re: Math Problem (easy, but I don't know)


Author:
shann
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Date Posted: 13:14:38 11/23/09 Mon

>A rectangle lot 30m by 20m is surrounded on all four
>sides by a concrete walk 3m wide. If you need to
>concrete only the sidewalk, how much concrete will you
>need? (surface area)

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[> Subject: Re: Math Problem (easy, but I don't know)


Author:
Isaac
[ Edit | View ]

Date Posted: 17:29:16 09/22/11 Thu

>A rectangle lot 30m by 20m is surrounded on all four
>sides by a concrete walk 3m wide. If you need to
>concrete only the sidewalk, how much concrete will you
>need? (surface area)

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Author:
Dr Kevin (Pain killers online)
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Date Posted: 05:00:09 05/16/11 Mon

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Subject: Beware of Racist Terrorist British and Canadians Terrorizing Asians in UK an Canada


Author:
Withikada
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Date Posted: 15:11:03 07/16/09 Thu


Beware of Racist Terrorists British and Canadians Terrorizing Asians in UK and Canada

VOLUNTEERS WELCOME TO SHARE THIS INFORMATION WITH OTHERS:

BEWARE OF RACIST COWARD TERRORIST BRITISH AND CANADIAN POLICE USING WALL SEE THROUGH TECHNOLOGIES AND AUDIO LISTENING IN DEVICES IN CONNIVANCE WITH NEIGHBOURS TO DEHUMANIZINGLY HARASS ASIANS IN THEIR HOMES WAILING SIRENS FROM OUTSIDE EACH TIME ASIANS MAKE ANY LIVING BODY MOVEMENTS IN THEIR OWN AND RENTED HOMES, WAKING, SLEEPING, GOING TO TOILET, EATING, PRAYING, ETC, FOR WOMEN AND MEN. TERRORIZING BRITISH POLICE ARE ABUSING THEIR UNIFORMS HARASSING ASIAN WOMEN AND MEN, YOUNG AND OLD, TO CREATE DISTURBANCE IN ASIANS LIVES THROUGH THE UNCOUTH RACISM AND JEALOUSY OF LOW CLASS TERRORIST BASTARD BRITISH AND CANADIAN POLICE HAVING NOTHING ELSE TO DO AND CREATING PURPOSEFUL HARASSMENT ABUSING THEIR STINKING UNIFORMS THROUGH SADISTIC BULLYING AGAINST HUMANS WHO ARE BETTER THAN THE LOW CLASS SCUMBAGS BRITISH AND CANADIAN TERRORIST POLICE.

THE TERRORIST WHITE RACISTS FORGET THAT THEY ROAMED AS UNCIVILIZED NAKED WILD SAVAGES IN THE FORESTS WHILE ASIANS WERE FAR BETTER CIVILIZED AND CULTURED OVER MANY YEARS OF ANCIENT CIVILIZATIONS THAT HAVE HELD AND NOT CRUMBLED AS THE WESTERN CIVILIZATIONS. GRABBING MATERIAL WEALTH THROUGH TWISTING THE WORD THROUGH APPLICATION OF EVIL SCHEMING INTELLECT AND COVETING AND SCREWING OTHER COUNTRIES RESOURCES THROUGH RESOURCE SNATCHING THROUGH WARS, ARM TWISTING BUSINESSES AND GUTLESS BOOTLICKERS IS NOT SUCCESS NOR EVERYTHING IN LIFE. THEIR BRUTE FORCE METHODS, GREEDY ALGORITHMS, GRREDY CAN OF WORMS, AND INFILTRATING INTO OTHERS PRIVACY METHODOLOGIES REFLECTS THEIR INNER UGLY CARICATURES EVEN IF OUTERLY SUGAR COATED AND ATTRACTIVE. THESE GO AGAINST THE VERY TEACHINGS OF THE SCRIPTURES.

ADDITIONALLY THE TERRORIST BRITISH AND CANADIAN POLICE ARE WAILING SIRENS TO PROVOKE ASIAN MALES WHEN ASIAN WOMEN GO TO TOILET IN THEIR PRIVATE HOMES AND APARTMENTS IN A PATTERN OF A WOLVES COMING OUT OF NOWHERE SUDDENLY TO WAIL SIRENS AND THEN FOLLOWING A PATTERN OF SILENCE WHILE THE ASIAN LADIES ARE NOT IN TOILET. IT HAS BEEN OBSERVED EACH TIME THE SIRENS ARE WAILIED THERE IS NO EMERGENCY. FURTHERMORE, THE TERRORIST BRITISH AND CANADIAN POLICE ARE IN CONNIVANCE WITH THEIR RACIST STOOGES TO HONK CARS WHEN THE TERRORIST BRITISH AND CANADIAN POLICE ARE UNABLE TO WAIL SIRENS WHEN ASIAN LADIES GO TO BATHROOM. THIS SHOWS THE INHERENT RACISM OF THE TERRORIST BRITISH AND CANADIAN POLICE PORTRAYING A NON-RACIST IMAGE OF THEMSELVES. THE BRITISH AND CANADIAN POLICE AND THEIR RACIST STOOGES ARE COMMITTING SEXUAL HARASSMENT OF ASIAN WOMEN AND MEN.

RACIAL HARASSMENT IS SERIOUS AND CAUSES ANGER, FEAR, DEPRESSION, CONFUSION, HELPLESSNESS, PHYSICAL AND MENTAL ILLNESSES AFFECTING RELATIONSHIPS OF PEOPLE AT HOME AND WORK. RACISM MEANS DISRUPTION OF FREEDOM. ANTI-CHRIST RACISTS AND THE RACIST POLICE BEHAVING RACISTLY COMMIT PRIVACY AND INFORMATION THEFT, BEHAVING AS CRIMINALS.

TERRORIST UK AND CANADA POLICE HARASSMENT OF PEOPLE IS SERIOUS DISRUPTION OF FREEDOM AND CAUSES ANGER, FEAR, DEPRESSION, CONFUSION, HELPLESSNESS, PHYSICAL AND MENTAL ILLNESSES AFFECTING RELATIONSHIPS OF PEOPLE AT HOME AND WORK. ANTI-CHRIST POLICE THEMSELVES COMMIT INFORMATION AND PRIVACY THEFT, BEHAVING AS CRIMINALS. THE TERRORIST RACIST WHITE POLICE AND THEIR COLORED GUTLESS INSIDERS-INFORMERS EMPOWER THEM TO ABUSE THEIR POWER AND HARASS PEOPLE.

BEWARE OF UGLY STINKING LOW CLASS DISHONEST RACIST ANTI-CHRIST TERRORIST BRITISH AND CANADIAN POLICE - PUBLIC SERVANTs IN STINKING UNIFORMS SURVIVING ON PULIC TAX PAYERS MONEY, BEHAVING AS RACIST WHITE SCUM-BAGS AND THE UGLY STINKING LOW CLASS RACIST WHITE DISHONEST ANTI-CHRIST BRITISH AND CANADIAN NEIGHBORS BOTH COMMITTING THE SERIOUS CRIME OF PRIVACY THEFT THROUGH ILLEGAL USE OF AUDIO AND WALL-SEE-THROUGH DEVICES IN OTHERS HOMES AND HACKING OF ONLINE INTERNET AND EMAIL AND LANDLINE AND CELL PHONES AND THEFT OF OFFLINE COMPUTER HARD-DRIVES USING EMR AND KEYLOGGER TECHNOLOGIES FROM NEIGHBORHOOD AND CARS OUTSIDE TO ILLEGALLY INFILTRATE INTO PRIVATE OFFLINE PERSONAL COMPUTERS HARD DRIVES IN PEOPLES HOMES.

THE TERRORIST BRITISH AND CANADIAN POLICE CANNOT BEAR TO BE WATCHED AND THEIR UGLY ANTI-CHRIST DEEDS EXPOSED. THEY FORGET DO UNTO OTHERS AS YOU WOULD HAVE OHTERS DO UNTO YOU. EVEN EDITING THESE LINES ON OFF-LINE COMPUTERS ALARMS THE EVIL DOERS AS THEIR UGLY DEEDS ARE BEING EXPOSED AND CAUSES THEM TO WAIL SIRENS. WATCH THE BRITISH AND CANADIAN POLICE:

DISHONEST RACIST ANTI-CHRIST TERRORIST BRITISH AND CANADIAN POLICE IN STINKING UNIFORMS PERPETUATE RACISM IN CONNIVANCE WITH RACIST ANTI-CHRIST WHITE DISHONEST BRITISH AND CANADIAN NEIGHBORS TO ILLEGALLY AND UNWARRANTEDLY USE WALL SEE THROUGH TECHNOLOGY, AUDIO LISTENING IN DEVICES, EMR VAN ECK PHREAKING EQUIPMENT, AND INTERNET, EMAIL, AND LANDLINE AND CELLPHONE TELEPHONE HACKING AGAINST ASIANS IN THEIR HOMES THROUGH WAILING SIRENS FROM OUTSIDE FOR EVERY LIVING BODY MOVEMENT OF ASIANS IN THEIR HOMES. INTERNET AND COMPUTER HACKING AND INFILTRATING INTO OTHERS PRIVACY IS A SERIOUS CRIME. THEY WAIL SIRENS AND HAVE THEIR INSIDERS IN CARS CREATE SOUND DISTURBANCE OF ACCELERATING AND HONKING AND NEIGHBORS BANGING DOORS AND THROWING THINGS EACH TIME THE EXPOSERS OF THEIR UGLY DEEDS MAKE LIVING MOVEMENTS AT HOME EVEN AT NIGHT AND DAY, EVEN DURING TOSSING AND TURNING IN BED, AND EVEN IN TOILET. THE SOLE PURPOSE OF THE ANTI-CHRIST DISHONEST RACIST TERRORIST BRITISH AND CANADIAN POLICE IS TO DISHONESTLY MAINTAIN LAW AND ORDER THROUGH ENSURING THAT THE RACIST WHITE DISHONEST BRITISH SHOULD BE ALLOWED TO DEHUMANIZINGLY DISTURB, INTIMIDATE, AND HARASS ASIAN MEN AND WOMEN IN THEIR HOMES AND ON STREETS, SHOPS, AND PUBLIC TRANSPORT THROUGH THE ILLEGAL USE OF THESE TECHNOLOGIES WITH POLICE CONNIVANCE AND TO INTIMIDATE, HARASS, DISTURB, AND PROVOKE ASIANS WHO REFUSE TO TOLERATE THIS ILLEGAL NONSENSE OF DISHONEST RACIST ANTI-CHRIST TERRORIST BRITISH AND CANADAIN POLICE IN CONNIVANCE WITH DISHONEST RACIST ANTI-CHRIST BRITISH AND CANADIAN NEIGHBORS REFLECTING THEIR VAMPIRE CULTURE DEVOID OF INTEGRITY. THEY FORGET THAT 'HE WHO LIVES BY THE SWORD DIES BY THE SWORD' - 'THOSE WHO PERPETUATE VAMPIRE CULTURE WILL DIE BY THE VAMPIRE CULTURE'.

ABUSING AND DISRESPECTING PRIVACY IS A HEINOUS CRIME. THE CONCEPT BEING PREACHED IS THAT 'WHY DOES ANYONE NEED TO WORRY ABOUT PRIVACY IF THEY HAVE DONE NOTHING WRONG'. THIS IS THE ANTI-CHRIST WAYS OF INFILTRATING SCUMBAGS TERRORIST BRITISH AND CANADIAN POLICE. WHY DOES ANYONE NEED PRIVACY?: WHY DOES EVERYONE DRESS? WHY DOESN'T EVERYONE GO NAKED? LACK OF PRIVACY IS SAME AS WALKING EVERYWHERE NAKED AS A STREAKER! ARE THE TERRORIST BRITISH POLICE PREACHING THE CONCEPT OF EVERYONE BECOMING STREAKERS - NAKED UNCIVILIZED PEOPLE EVERYWHERE IN UK AND CANADA? JUST SO THE TERRORIST BRITISH AND CANADIAN POLICE CAN RETAIN THEIR ABUSE OF POWER THROUGH PROCLAIMING AN INFLATED, MANUFACTURED, FALSE, SELF-INITIATED SELFISH CONCEPTS OF SO-CALLED TERROR THREATS AND GAME PLAYING WAILING SIRENS AS EMPTY VESSELS MAKING MORE NOISE IN THEIR ILLEGAL ATTEMPT TO CREATE SOCIAL CONTROL THAT IS MAINLY A SOCIAL NUISANCE. THE POLICE AUTHORIZE UNCOUTH RACIST WHITE NEIGHBORS TO CREATE A SMOKE SCREEN FOR THE POLICE TO WAIL SIRENS AND NEIGHBORS TO CREATE LOUD DISTURBANCE AT APPROPRIATE TIMES CORRESPONDING TO ASIANS WORKING ON THEIR OFFLINE COMPUTERS, CONNECTING TO INTERNET, MAKING PHONE CONVERSATIONS ON LANDLINE AND CELLPHONES, AND WHILE EATING, SLEEPING, TOILET, WORKING, LOOKING OUT THE WINDOWS, OPENING CLOSING CURTAINS AND BLINDS, SWITCHING ON AND OFF LIGHTS, ETC. THE RACIST WHITE BRITISH AND CANADIANS ARE FULL OF INFERIORITY COMPLEX THEMSELVES DUE TO THEIR IMPROPER UPBRINGING THAT IS REFLECTED IN THEIR WHITE RACIST SCUMBAG BEHAVIOUR OF INHERENT RACIAL INTOLERANCE OF THE ASIANS IN CONNIVANCE WITH RACIST WHITE SCUMBAG POLICE.

ABUSING PRIVACY AND HARASSING HUMANS - LIVING CREATURES OF GOD, IS HARMFUL TO MIND, BODY AND SOUL. THUS, THE TERRORIST BRITISH AND CANADAIN POLICE HAVE BECOME THE PERFECT ANTI-CHRIST. THEY WILL BE DEBARRED FROM THE KINGDOM OF GOD. EVADING TACTICS SUCH AS WHERE IS GOD, ETC, WILL NOT ABSOLVE THEM OF THEIR SINS AND THE BRITISH AND CANADIAN POLICE WILL NOT GO UNPUNISHED FOR THEIR HEINOUS CRIMES OF ABUSING PRIVACY.

THE TERRORIZING BRITISH AND CANADIAN POLICE ARE ADDITIONALLY USING HIDDEN LONG-DISTANCE CAMERAS FROM STRATEGIC POSITIONS TO TARGET THOSE WHO EXPOSE THEIR UGLY DEEDS. USING THESE CAMERAS, THEY BEAM THE VIDEO IMAGES TO THEIR POLICE CARS ROAMING WASTEFULLY WITH THEIR BACKS TO THE TARGETTED PEOPLE. AFTER THEIR AFOREMENTIONED UGLY DEEDS WERE EXPOSED, THEY PRETENDED NOT TO BE COWARDS THROUGH AVOIDING ROAMING WITH THEIR BACKS TO THE TARGETTED PEOPLE AND INSTEAD APPROACHING FROM FRONT. HOWEVER, THE FACT THAT THEY ARE COMMITTING THEIR HEINOUS CRIMES OF VIOLATING OTHER HUMANS PRIVACY THROUGH EVIL MEANS AND INSIDER INFORMERS AMID NEIGHBORS REFLECTS THEIR COWARDICE AND STILL MAKES THEM ABSOLUTE LOW CLASS COWARDS COWARDS COWARDS COWARDS. COWARDS ARE A SHAMEFUL DISGRACE FOR HUMANITY. THUS, THE TERRORIST BRITISH AND CANADIAN POLICE ARE THE ANTI-CHRIST COWARDS HARASSING THOSE WHO EXPOSE THE UGLY DEEDS OF POLICE HARASSMENT AND INVASION INTO PRIVACY OF PEOPLE AT HOME AND WORK, THROUGH VISIBLE AND INVISIBLE AUDIO AND VIDEO DEVICES, WALL SEE THROUGH TECHNOLOGIES, OFFLINE COMPUTER HACKING USING KEY LOGGERS AND ELECTRO MAGNETIC RADIATION (EMR) EQUIPMENT TO RETRIEVE IMAGES OF ANYTHING BEING TYPED ON PERSONAL COMPUTERS OFFLINE AT HOME AND WORK, AS WELL AS ONLINE COMPUTER HACKING THROUGH THE INTERNET, THROUGH ILLEGAL ACCESS UNDER THE FALSE PRETEXT OF SURVEILLANCE AND PROTECTION AND SECURITY, THEREBY VIOLATING PEOPLES HUMAN RIGHTS AND PRIVACY, INVADING THEIR LIVES AND CREATING DISTURBANCE AND HARASSMENT, ABUSING THEIR DUTY OF CARE FOR THE PEOPLE AND CAUSING PEOPLE PERSONAL INJURIES (MIND, BODY, AND SOUL) THAT WILL WEIGH HEAVILY UPON THEM IN THE JUDGMENT OF THE ALMIGHTY LORD OF CREATION THAT LEAVES NO WRONGS GO UNPUNISHED EVER!


http://www.policeuniformshame.blogspot.com

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http://www.youtube.com/watch?v=gSv4XZSR5ZI

http://www.jihadwatch.org/archives/024365.php

http://www.youtube.com/watch?v=p6V3oUoffCE

http://www.youtube.com/watch?v=1N3ySmBP5ds

http://www.youtube.com/watch?v=wnhiRS37eFc

http://www.religionnewsblog.com/4750

http://www.religionnewsblog.com/4750/police-officers-racist-shame

http://uk.news.yahoo.com/4/20090610/tuk-met-police-officers-suspended-over-t-dba1618.html

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http://www.boingboing.net/2008/07/22/racist-cop-uses-uk-t.html

http://www.theanswerbank.co.uk/Law/Question538287.html

http://www.privacyhackers.blogspot.com

http://www.ukcorruptiontoday.com/index_files/page0019.htm

http://video.google.co.uk/videosearch?hl=en&q=police+harassment&um=1&ie=UTF-8&ei=Q9L0Sf7YKKSOjAf-ya23DA&sa=X&oi=video_result_group&resnum=4&ct=title#

http://www.countercurrents.org/uk-ingram120805.htm

http://www.articlearchives.com/international-relations/national-security/1790326-1.html

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http://blogcritics.org/archives/2005/09/08/145937.php

http://yourprivacyandyou.webs.com/Your%20privacy,%20Your%20Personal%20Information%20and%20You.ppt

http://www.ephotozine.com/topic/t-54561

http://clearerchannel.org/drupal/?q=aggregator/sources/9

http://www.atlanticfreepress.com/news/1/997-untamed-atrocity-qcreative-destructionq-at-work-in-baghdad.html

http://www.mcb.org.uk/media/presstext.php?ann_id=53

http://www.weeklygripe.co.uk/a430.asp

http://www.pickledpolitics.com/archives/2224

hhttp://www.wsws.org/articles/2005/aug2005/race-a12.shtml

http://news.bbc.co.uk/1/hi/uk/257693.stm

http://www.socialistworker.co.uk/art.php?id=15457

http://www.greenpeace.org.uk/blog/about/dont-let-police-intimidate-you-20090414

http://digg.com/world_news/How_British_Police_Are_Criminalizing_Peaceful_Protest

http://uk.answers.yahoo.com/question/index?qid=20090416150247AA1Ts4l

http://newsgroups.derkeiler.com/pdf/Archive/Soc/soc.culture.british/2007-02/msg00097.pdf

http://www.just-a-regular-guy.com/2009/01/12/british-police-turn-tail-and-run-from-islamic-protesters/

http://www.reddit.com/r/technology/comments/7n7bs/british_police_set_to_step_up_hacking_of_home_pcs/


Burke, J. and Warren, P. (2002). How mobile phones let spies
see our
every move. The Observer, October 13.
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Bush, Steve. (2002, August 12). Radar with Cell Phones? Look at
CellDar.
http://3nw.com/pda/radar_with_cell_phones__look_at_celldar.htm

Bush, Steve. (2006, November 17). Police will use radar to see
through walls. Electronics Weekly.
http://www.electronicsweekly.com/Articles/2006/11/17/40181/Police+will+use+radar+to+see+through+walls.htm

Chan, Hans, H. (1999, June 4). Cops have eyes on x-ray vision.
New technology would let police see through walls. New York:

APBNews.com.
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walls.
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Hunt, A., Tillery, C., & Wild, N. (2001). Through-the-wall
surveillance technologies. Corrections Today, 63(4), 132.

Kuhn, M. G., & Anderson, R. J. (1998). Soft tempest: Hidden data
transmission using electromagnetic emanations
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Lamb, G. M. (2006). Does digital age spell privacys doom?
Christian Science Monitor, 98(149).

Lyon, D. (2001c). Surveillance after September 11. Surveillance
after September 11.
Sociological Research Online 6(3).
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Marx, G. T. (1986). The iron fist and the velvet glove:
Totalitarian potentials within democratic structures.
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Marx, G. T. (2001). Murky conceptual waters: The public and the
private. Ethics and Information Technology, 3(3), 157-159.
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McGowan, Dave. (2000, June). Sonys Magic cameras.
http://www.davesweb.cnchost.com/cameras.htm

Mejia, R. (2002). More surveillance on the way. The Nation,
October 30.
http://www.thenation.com/doc/20021111/mejia20021030

Miles, Donna (2006, January 3). New device will sense through
concrete walls. American Forces Information Service. US Department of
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Sanders, Jane (2001, April 12). Flash of force: Radar flashlight
could help police detect suspects hiding behind doors and 8-inch thick
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Simonite, Tom. (2006, November 14). Compact radar tracks
movement through a wall. New Scientist.
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human security?
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Alder, G.S. and Ambrose, M.L. (2005b). An examination of the effect of computerized performance monitoring feedback on monitoring fairness, performance, and satisfaction. Organizational Behavior and Human Decision Processes, 97: 161177.

Alge, B.J. (1999). The role of fairness and privacy in electronic performance monitoring and control systems: some preliminary findings. Paper presented at the 1999 Annual
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Alge, B.J. (2001). Effects of computer surveillance on perceptions of privacy and procedural justice. Journal of Applied Psychology, 86: 7, 797804.

Alge, B.J. and Ballinger, G. (2001). Electronic workplace surveillance: the effects of advanced notice and task discretion on perceptions of privacy and procedural justice. Paper presented at the 2001 Meeting of the Society for industrial/Organizational Psychology, San Diego, CA, April.

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When unfairness matters most: supervisory violations of electronic monitoring practices Human Resource Management Journal, Vol 17, no 3, 2007, pages 227247


THE EXPOSURE OF THE UGLY DEEDS OF THE TERRORIST BRITISH AND CANADIAN POLICE HAS PUNCHED THE TERRORIST BRITISH AND CANADIAN POLICE THAT IS REFLECTED IN THEIR SCREAMING WAILING SIRENS AND USING THEIR INSIDER INFORMERS IN THE NEIGHBORHOOD TO INFILTRATE INTO INTERNET AND HONK CAR HORNS AND TALK LOUDLY IN NEIHGBORHOOD HACKING INTERNET EACH TIME THEIR UGLY DEEDS OF USING WALL SEE THROUGH TECHNOLOGIES, AUDIO LISTENING DEVICES, LANDLINE PHONES, CELLPHONES AND INTERNET HACKING ARE BEING EXPOSED.

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Subject: The equation y=a(x-h)^2-k


Author:
Kayanachan
[ Edit | View ]

Date Posted: 16:40:55 04/24/07 Tue

I'm having some trouble with my math homework. I can't seem to figure what h and k are in the equation y=a(x-h)^2-k. Any one know?

[ Post a Reply to This Message ]
[> Subject: Re: The equation y=a(x-h)^2-k


Author:
Suzie
[ Edit | View ]

Date Posted: 15:57:54 10/28/08 Tue

>I'm having some trouble with my math homework. I can't
>seem to figure what h and k are in the equation
>y=a(x-h)^2-k. Any one know?

(h,k) is the vertex of the parabola, h is the point on the x- axis and k is the point on the y-axis

[ Post a Reply to This Message ]
Subject: Geometry- proof


Author:
LV
[ Edit | View ]

Date Posted: 14:21:25 06/03/04 Thu

Hello
I am needing help with a proof... actually just needing some guidance as to where to start! I have to prove the following in as many ways as possible: Given a triangle ABC with median AD, prove that 2((AB^2)+(AC^2))= BC^2 + 4(AD^2). I have proven this using analytic methods... and that will barely get me a passing mark. Any ideas?

[ Post a Reply to This Message ]
[> Subject: Re: Geometry- proof


Author:
mik
[ Edit | View ]

Date Posted: 16:26:28 11/18/05 Fri

hi.. i am having trouble figuring out what iam trying to prove in this question: In triangle ABC, A(o,a) B(0,0) and C (b,c) , using hte analytic method, prove that the right bisectors of the sides meet at a common point.

[ Post a Reply to This Message ]
[> [> Subject: Re: Geometry- proof


Author:
QUITTNER
[ Edit | View ]

Date Posted: 08:23:07 11/21/05 Mon

>>> In triangle ABC, A(o,a) B(0,0) and C (b,c) , using hte analytic method, prove that the right bisectors of the sides meet at a common point. <<<
..... A to B is a vertical line, C is further to the right.
..... Find the equation of the line AC, then the equation of its right-angled bisector.
.....Do the same with AB (a horizontal line). At which point does it meet the bisector line you found?
..... Then do the same with line BC. At which point does it meet the other 2? Prove that it is the SAME point.

[ Post a Reply to This Message ]
[> Subject: Re: Geometry- proof


Author:
mik
[ Edit | View ]

Date Posted: 16:26:37 11/18/05 Fri

hi.. i am having trouble figuring out what iam trying to prove in this question: In triangle ABC, A(o,a) B(0,0) and C (b,c) , using hte analytic method, prove that the right bisectors of the sides meet at a common point.

[ Post a Reply to This Message ]
[> Subject: Re: Geometry- proof


Author:
Ladricka Brown
[ Edit | View ]

Date Posted: 12:41:22 02/12/06 Sun

>Hello
>I am needing help with a proof... actually just
>needing some guidance as to where to start! I have to
>prove the following in as many ways as possible: Given
>a triangle ABC with median AD, prove that
>2((AB^2)+(AC^2))= BC^2 + 4(AD^2). I have proven this
>using analytic methods... and that will barely get me
>a passing mark. Any ideas?

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[> Subject: Re: Geometry- proof


Author:
Ladricka Brown
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Date Posted: 12:44:52 02/12/06 Sun

>Hello
>I am needing help with finding numbers in 30-60-90 right triangle and a 45-45-90 triangle as well as angles of elevation and depression, think u could help me out? It would mean a great deal to me if u could help me out>

Thanks, Ladricka Brown

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[> [> Subject: Re: Geometry- proof


Author:
Esperanza Arriaza
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Date Posted: 19:59:16 02/16/06 Thu

>>Hello
>>I am needing help with finding numbers in 30-60-90
>right triangle and a 45-45-90 triangle as well as
>angles of elevation and depression, think u could help
>me out? It would mean a great deal to me if u could
>help me out>
>
> Thanks, Ladricka Brown

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[> [> Subject: Re: Geometry- proof


Author:
Mohammed Adams (angles of elevation and depression)
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Date Posted: 08:14:38 07/23/07 Mon

i am having problem in solving a particular topic in mathematics and this topic include Angles of elevation and depression.




Thanks,from Adams

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Subject: Need help with Quadratic Equations


Author:
Robin
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Date Posted: 16:55:58 11/20/06 Mon

For the function y=x^2-4x-5 perform the following task:

Put the function in the form y=a(x-h)^2+k

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Subject: parametric equation


Author:
adeela (required equation for rounded arch)
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Date Posted: 08:37:39 09/11/06 Mon


i want to draw a figure in OPENGL computer graphics. may task is to make rounded arch pointed arch and an ogee arch for that i required a parametric equation.

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Subject: Amount


Author:
Randy
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Date Posted: 23:59:40 07/14/06 Fri

Calculate the amount of rainfall (in inches) needed to put 100,000 gallons of water over an area of 3.76 acres.

Thanks for your assistance.

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Subject: Area and Percent


Author:
Randy
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Date Posted: 19:12:54 07/06/06 Thu

Calculate the area of the largest circle that can be cut from a rectangular sheet of metal and the percent of the rectangle wasted.

Dimensions of sheet: Length- 11 in.

Width- 8.5 in.

Thanks for your assistance.

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[> Subject: Re: Area and Percent


Author:
QUITTNER
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Date Posted: 11:20:30 07/10/06 Mon

Calculate the area of the largest circle that can be cut from a rectangular sheet of metal and the percent of the rectangle wasted.
Dimensions of sheet: Length- 11 in., Width- 8.5 in.
..... The diameter of the largest possible circle is the same as length of the width of the rectangle.
Calculate the area of the circle. (ANSWER 1)
Calculate the area of the rectangle.
Deduct the area of the circle from the area of the rectangle, that difference is the wasted area.
Get that wasted area in terms of a percentage of the total area of the rectangle. (ANSWER 2)
..... Good luck!

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Subject: Geometry


Author:
Heather C.
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Date Posted: 13:54:31 04/25/06 Tue

If two polygons are similar with lengths of corresponding sides in the ratio of a:b, then the ratio of their perimeters is ________and the ratio of their areas is
__________.

Please help me fill in the blanks!

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Subject: What is the equation for understanding message boards?


Author:
Jim Jefferson
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Date Posted: 07:23:04 12/08/05 Thu

This is a test


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[> Subject: Re: What is the equation for understanding message boards?


Author:
QUITTNER
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Date Posted: 11:19:16 12/08/05 Thu

Calculate the time required to drain the whole body of enough blood to stop the bloody picture from repeating itself. Plot your results.
..... This test is due yesterday. [LAUGHS]

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Subject: Vertex of Parabola


Author:
Wira Maya Tio
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Date Posted: 19:54:08 07/21/05 Thu

Please help?! I have 2 horizontally aligned points, and need to find the vertex of the parabola. Additional information known is that the half curve length of the parabola must be L.

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[> Subject: Re: Vertex of Parabola


Author:
fizixx
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Date Posted: 17:52:41 12/01/05 Thu

>Please help?! I have 2 horizontally aligned points,
>and need to find the vertex of the parabola.
>Additional information known is that the half curve
>length of the parabola must be L.

This is not enough information for anyone to solve this for you. You need to supply more detail. Saying that you have two points aligned along a horizontal is insufficient. Do you have values for these points? In other words, do you know their cardinal points? For example; (2,4).....or....(-1,5). Like that.

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Subject: I like your website. Good design, pretty navigations.


Author:
Juli
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Date Posted: 13:59:04 07/22/05 Fri

I like your website. Good design, pretty navigations.
mortgage

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Subject: Parabola


Author:
FB
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Date Posted: 15:39:19 06/06/05 Mon

Ok i am having a parabola problem i think i drew it right but im not sure. Anyways here is the question:

A masonry bridge over a river has an arch in the form of a parabola with a vertical axis. The widths of the arch at water level are 5m above water level and 12m and 8m respectively. Find the height of the arch above the point at water level which is 2m from the middle.

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[> Subject: Re: Parabola


Author:
QUITTNER
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Date Posted: 08:17:07 06/10/05 Fri

>>> A masonry bridge over a river has an arch in the form of a parabola with a vertical axis. The widths of the arch at water level are 5m above water level and 12m and 8m respectively. Find the height of the arch above the point at water level which is 2m from the middle. <<<
..... A shortened form of the equation with the origin (x=0 and y=0) at the top of the arch is
y = p * x^2 with all y being negative.
..... Put y1 at x=2, put y2 at x=4, and y3 at x=6. The x of y2 and y3 are half the total widths.
..... We also know that (y2 - y3) = 5 (IS THAT RIGHT?) where y3 is the water level.
..... Insert into the equations y=p*x^2 where * means times, and ^2 means squared:
y3=6*6*p=36p, y2=16p, and y2-y3=5. Solve for p and you then can get y1, y2 and y3. The required height above water level is y1-y3 where x=2.

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Subject: i need the area of the overlapping parts


Author:
randy
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Date Posted: 19:19:51 03/24/05 Thu

two overlapping squares, one at a 59-degree angle to the other. The larger of the two squares is 180 meters on a side, and the smaller of the two is 162 meters on a side. The corner point of the larger square is at the center point of the smaller square.

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Subject: Books on Maple and Statistics


Author:
Academy
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Date Posted: 05:57:01 12/19/04 Sun

A carefully prepared and well-written book

http://writers.fultus.com/aladjev/book01.html

without doubt can be recommended as a very valuable manual and textbook for a Maple user who is looking for a mainly textbook which combines programming manual with a presentation of widely applicable new Maple means.

The following web site:

http://writers.fultus.com/aladjev/book02.html

presents a new book on General Theory of Statistics.

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[> Subject: Re: Books on Maple and Statistics


Author:
QUITTNER
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Date Posted: 06:35:26 12/20/04 Mon

Thanks for the info. Do have a MERRY CHRISTMAS and/or other happiness at this greetings season, and a healthy and happy whole NEW YEAR 2005! Health is more important than money.

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Subject: finding equation of parabola going through 3 points


Author:
soule
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Date Posted: 23:11:21 11/30/04 Tue

im having a hard time solving this problem. Can somebody help? it says. Find an equation for the parabola with horizontal axis of symmetry if it passes though points (5,0) (14,1) and (5,-2)

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[> Subject: Re: finding equation of parabola going through 3 points


Author:
QUITTNER
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Date Posted: 12:12:25 12/03/04 Fri

>>> Find an equation for the parabola with horizontal axis of symmetry if it passes though points (5,0) (14,1) and (5,-2) <<<
..... As I remember it, the equation for a parabola with HORIZONTAL axis of symmetry is
(y-a) squared = k times (x-b)

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[> [> Subject: Re: finding equation of parabola going through 3 points


Author:
QUITTNER
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Date Posted: 07:25:39 12/06/04 Mon

>>>> Find an equation for the parabola with horizontal
>axis of symmetry if it passes though points (5,0)
>(14,1) and (5,-2) <<<<
>>> ..... As I remember it, the equation for a parabola with HORIZONTAL axis of symmetry is (y-a) squared = k times (x-b) <<<
..... Normally from this point on you substitute the 3 x and the 3 y of the 3 points given into 3 simultaneous equations, and then solve for the 3 unknown variables a,b,and k.
HOWEVER, in this particular example there is an easier way:
..... Note that two of the given points have the SAME x, with their y being 0 and -2. This means that the axis of symmetry is half-way between these y, namely -1. But the vertex is on this axis, so that the vertex, too, has y=-1
..... In the equation on its left side it says (y-a)^2, and the a represents the y of the vertex, which we know now as being -1 = a. And on the right side of the equation b is the x of the vertex. That means that the new equation, for this example only, is:
(y+1) squared = k times (x-b) which is (y+1)^2=k*(x-b)
Now there are only 2 unknown variables, k and b, and you need now only 2 equations to solve for them:
(0+1)^2 = k*(5-b) for point (5,0)
(1+1)^2 = k*(14-b) for point (14,1)
Always check your results.

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Subject: calculate a parabola from 5 diff points


Author:
guy
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Date Posted: 02:07:44 05/26/04 Wed

hi i need some help im trying to find an algorithm for
finding the equation of a parabola from 5 diff points
thanks for your time!!!
guy

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[> Subject: Re: calculate a parabola from 5 diff points


Author:
QUITTNER
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Date Posted: 10:19:03 05/27/04 Thu

>>> hi i need some help im trying to find an algorithm for finding the equation of a parabola from 5 diff points thanks for your time!!! guy <<<
..... A parabola is fully described by only 3 points. If you are given more than 3 points then you could use "the least squares method" to find the closest approximate parabola, meaning finding a parabola whose value at a given x, call it y, is a distance, call it d, away from a given point at that x, with the sum of all the (d squared) being at a minimum. Is that what you want?

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[> [> Subject: Re: calculate a parabola from 5 diff points


Author:
QUITTNER
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Date Posted: 11:36:38 06/17/04 Thu

By the way, some people use A+Bx+Cx^2 as a general equation of what they call a parabola.
..... A REAL parabola is NOT the same as that, but is defined as a curve, all of whose points are at the SAME distance from a given line and from a given point, called the "Focal Point". The equation of a special kind of parabola is (y-A)^2=K*(x-B), with, in an even more special case, A and B are both zero.
..... If there are 3 unknowns then you need 3 simultaneous equations to solve (can be quite dificult!) for these unknowns.

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Subject: Inverse of Polynomial Function


Author:
tnewton
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Date Posted: 17:40:43 02/17/04 Tue

What I would really like to do is find the coefficients of INV(f(x)) from the coefficients of f(x) of an nth degree polynomial (1-variable).

f(x)= SUM(ai * x^i) for i = 0..n)
INV(f(x)) = ???


Any and all help is greatly appreciated. Thanks!

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[> Subject: Re: Inverse of Polynomial Function


Author:
QUITTNER
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Date Posted: 10:22:18 04/23/04 Fri

>>>What I would really like to do is find the coefficients of INV(f(x)) from the coefficients of f(x) of an nth degree polynomial (1-variable).<<<

>>> f(x)= SUM(ai * x^i) for i = 0..n)
>INV(f(x)) = ??? <<<
..... As I remember it, if y is a function of the sum of various degrees of x, then the inverse is (simply - oh yeah?) x as a function of y. That may be quite difficult to find is many cases involving higher than the 3rd degree of x.

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[> [> Subject: Re: Inverse of Polynomial Function


Author:
tnewton
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Date Posted: 19:39:51 05/04/04 Tue

Yes, that's the definition of inverse, but it requires you to know the order of the function first in order to solve. I believe there may be some algorithm to find the reverse coefficients regardless of degree, and may require very deep recursion (related to the polynomial order); at least that's the direction I seem to keep finding myself heading. I've seen a process that finds the solution to the inverse function; it's a little tough to follow and I haven't been able to use it as a basis for determining the coefficients. Maybe if I figure this out I'll get my name in the history books...
>>>>What I would really like to do is find the
>coefficients of INV(f(x)) from the coefficients of
>f(x) of an nth degree polynomial (1-variable).<<<
>
>>>> f(x)= SUM(ai * x^i) for i = 0..n)
>>INV(f(x)) = ??? <<<
>..... As I remember it, if y is a function of the sum
>of various degrees of x, then the inverse is (simply -
>oh yeah?) x as a function of y. That may be quite
>difficult to find is many cases involving higher than
>the 3rd degree of x.

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[> [> [> Subject: Re: Inverse of Polynomial Function


Author:
QUITTNER
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Date Posted: 10:42:17 05/06/04 Thu

tnewton, unfortunately I can't help you with that. But maybe you'll come up with some useful solution(s). Good luck, and keep well!

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Subject: conics


Author:
cheekz
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Date Posted: 15:02:13 01/18/04 Sun

The cables of the suspension bridge hang in a curve that approximates a parabola. The road passes through the vertex. The supporting towers are 550 m apart and 50 m high. Write and equation for the parabola

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[> Subject: Re: conics


Author:
QUITTNER
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Date Posted: 12:37:21 01/19/04 Mon

>>> The cables of the suspension bridge hang in a curve that approximates a parabola. The road passes through the vertex. The supporting towers are 550 m apart and 50 m high. Write and equation for the parabola. <<<
..... Assuming that the vertex is at the origin (0,0), the equation of the parabola is
y^2 = 2 a x - Find a
..... The vertex is where the cables hit the road level, and it's a symmetic graph. The top of the tower on the right is at (275,50). Substitute into the equation to find a.

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Subject: Mathematics related to taxes


Author:
Maria
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Date Posted: 18:32:51 10/16/03 Thu

I have been working on an LCX assignement for the past few days, and yet, I'm still stumped. the problem is quite simple, it consists of talking the total price of an object and find the initial value; before taxes have been added to the price. If the Total is 80.20$ and we know that the initial price is taxed once at 7%, compounded and taxed again, at a rate of 7.5%, what is the initial price of the item?

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[> Subject: Re: Mathematics related to taxes


Author:
Maria
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Date Posted: 18:35:22 10/16/03 Thu

>I have been working on an LCX assignement for the past
>few days, and yet, I'm still stumped. the problem is
>quite simple, it consists of taking the total price
>of an object and find the initial value; before taxes
>have been added to the price. If the Total is 80.20$
>and we know that the initial price is taxed once at
>7%, compounded and taxed again, at a rate of 7.5%,
>what is the initial price of the item?

By the way, if you could include a detailed solution, i would very much appreciateit.

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[> [> Subject: Re: Mathematics related to taxes


Author:
QUITTNER
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Date Posted: 08:37:50 10/31/03 Fri

Subject: Mathematics related to taxes
Author: Maria Date Posted: 18:32:51 10/16/03 Thu
>>> I have been working on an LCX assignement for the past few days, and yet, I'm still stumped. the problem is quite simple, it consists of talking the total price of an object and find the initial value; before taxes have been added to the price. If the Total is 80.20$ and we know that the initial price is taxed once at 7%, compounded and taxed again, at a rate of 7.5%, what is the initial price of the item? <<<
..... If the item would have been taxed once at 7%, then to find the initial price before taxes if the total price is 80.20, then divide 80.20 by one plus 7 hundreds. That is 80.20/1.07=74.95. Check this by using a calculator 74.95 + 7%=80.20 (rounded), OK
..... If something is compounded then you have to know also the time(s) involved, which is NOT given here.

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Subject: + Save 75% on printer ink! Click Here!


Author:
LowCostInk
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Date Posted: 13:42:56 10/05/03 Sun






Don't keep paying for inkjet cartridges when you can refill them for a fraction
of the price!



CLICK HERE!

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Subject: + Save 75% on printer ink! Click Here!


Author:
LowCostInk
[ Edit | View ]

Date Posted: 13:26:14 10/05/03 Sun






Don't keep paying for inkjet cartridges when you can refill them for a fraction
of the price!



CLICK HERE!

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Subject: Distance/ Time


Author:
Randy
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Date Posted: 14:13:05 12/31/02 Tue

A steel railroad track is struck with a hammer at one end and sound waves are observed at the other, both along the track and through the air. What is the time interval (sec.)between the two sounds as heard by the observer? How long is the track? (The speed of sound in steel is assumed to be 16,000 fps.)

Please give step by step solution. Thanks for your assistance.

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[> Subject: Re: Distance/ Time


Author:
QUITTNER
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Date Posted: 10:49:33 02/18/03 Tue

You wrote: >>> How long is the track? (The speed of sound
>in steel is assumed to be 16,000 fps.) <<<
..... Some information is missing. You also must know: What is the speed of sound in the air? The difference between the two sound speeds is a clue; it's also in feet per second.
1) If you know the length of the track then you divide that length by the speed difference (feet/(feet/second)) to get the difference between the sounds in seconds.
2)If you know the time difference between the two sounds then you multiply the speed difference by the time difference between the two sounds to get the track length in feet (seconds times (feet per second)).

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[> Subject: Re: Distance/ Time


Author:
Enrico D.
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Date Posted: 23:32:33 03/15/03 Sat

>A steel railroad track is struck with a hammer at one
>end and sound waves are observed at the other, both
>along the track and through the air. What is the time
>interval (sec.)between the two sounds as heard by the
>observer? How long is the track? (The speed of sound
>in steel is assumed to be 16,000 fps.)
>
>Please give step by step solution. Thanks for your
>assistance.
If the railroad makes a curve, better a circle, the sound will arrive forst by air than by steel....

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[> Subject: rotation


Author:
Tina
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Date Posted: 12:22:14 10/04/03 Sat

A car goes on a 20,00-mile trip. the tires, including the spare, are rotated every 4,000 miles, so that the fire tires were used for an identical numer of miles. How many miles was each tire monted on the care, in use and is there another way of simplifying the problem?
>
>Please give step by step solution. Thanks for your
>assistance.

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Subject: Calculus


Author:
xncuiw
[ Edit | View ]

Date Posted: 21:39:35 10/02/03 Thu

Find the x-coordinates of the points on the hyperbola xy=1 where the tangets from teh point (1,-1) intersect the curve.

-plz give a step solution, I know what the answer is(from back of book), but I don't know how to do it. answer = -1+-root2

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Subject: Help in understanding set theory problems


Author:
Pete Snyder
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Date Posted: 04:38:25 05/05/03 Mon

Hello- I would like to ask you if you would please help me solve the two following problems. I have looked through many textbooks at my community college library. The frustrating part is that the books present information in an abstract sense, where no real numbers are used to solve the problems. Highly abbreviated equations are used and then 40-50 problems are given at the end of each section. No detailed examples are given in order to use as templates to solve the exercise problems. Would somebody please be able to provide detailed solutions to the following two problems. I would then be able to use these as examples (or templates) in order to understand what is being presented in the mathematics textbooks for these kinds of exercises. Also-please let me know how to actually say or verbalize the following equations. Thank you very much!

1. Let y and z be non-zero integers.
Show mathematical proof that if (3y, 10z) = 9, then x|(y,z). I need a proof and not just a numerical answer.

2. Let G be the following group of permutations.
G = {(3), (1234), (13)(24), (1432), (24), (12)(34), (13), (14)(23)}.
Let H = {(1), (1234), (13)(24), (1432)}.
Prove H is cyclic and find all the cosets of H in G.

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[> Subject: Re: Help in understanding set theory problems


Author:
QUITTNER
[ Edit | View ]

Date Posted: 15:28:09 05/05/03 Mon

Sorry, I don't know how to solve these problems. Are you aware of the many books in the SCHAUM OUTLINE SERIES on different mathematical topics? I like their many worked examples showing you how to solve problems, in addition to the theory. Good luck and have fun!

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[> Subject: Re: Help in understanding set theory problems


Author:
Lynn
[ Edit | View ]

Date Posted: 14:37:34 07/16/03 Wed

I assume that since you posted a couple of months ago, that if I'm answering assignment questions, it's too late. So, just so you can actually see how this is done, here we go:
(Incidentally, Shawm's is not too good at showing worked out solutions to problems that need proofs rather than numbers.)

>1. Let y and z be non-zero integers.
>Show mathematical proof that if (3y, 10z) = 9, then
>x|(y,z). I need a proof and not just a numerical
>answer.

Verbally: "If the greatest common divisor of 3y and 10z is nine, then find a factor of the greatest common divisor of y and z? (I'm paraphrasing a bit since as you typed it, it makes no sense.)

x = 3.

Proof (in words, sort of):

The fact that 9 is the greatest common divisor of 3y and 10z means two things: 1) that 9 divides both 3y and 10z.
and 2) that nothing bigger than 9 (no multiple of 9) also divides them.

So, let's see what we get out of consequence 1:
If 9|3y then it's clear that 3|y.
If 9|10z then 9 must divide z since 9 and 10 share no common factors.

Since 3|y and 3|9|z, we have that 3|(y,z).

In point of fact, using consequence 2 and the same sort of logic, it's possible to prove that 3 = (y,z)

Now, that's not how I would hand it in (although if marking it, I would sigh and give full marks).

What I would hand in:
Claim: 3|(y,z).
Proof:
9 | 3y (by hypothesis)
Thus, 3 | y (by dividing both sides by 9)

9 | 10z
(9,10) = 1
Thus, 9 | z (using the unique factorization theorem)
(This step may require more work, depending on how many consequences of the UFT you've seen in class.)
3 | 9
Thus 3 | z (transitivity)

Since 3|y and 3|z, then 3|(y,z).
QED
>
>2. Let G be the following group of permutations.
>G = {(3), (1234), (13)(24), (1432), (24), (12)(34),
>(13), (14)(23)}.
>Let H = {(1), (1234), (13)(24), (1432)}.
>Prove H is cyclic and find all the cosets of H in G.

(First, I assume that the first permutation in G is (1). Otherwise, it's not a group and nothing makes sense.)

The first part is fairly simple. To prove that a group is cyclic, all you need is to find a generator and then prove that that generator works. Since H has only 4 elements, trial and error should be quite quick.

So my solution would go as follows:
Claim: g:=(1234) is a generator of H.
Proof: Let this group act on the "word" abcd.

g(abcd) = dabc
g^2(abcd) = g(dabc) = cdab = [(13)(24)](abcd)
(ie, g^2 = (13)(24) )
g^3(abcd) = g(cdab) = bcda = [(1432)](abcd)
(ie, g^3 = (1432) )
g^4(abcd) = g(bcda) = abcd = [(1)](abcd)
(ie, g^4 = (1))
QED

The second part is also comparatively straight forward. A subgroup always divides the big group into equal parts when you take cosets. Furthermore, these equal parts are the same size as the subgroup. So, since H has 4 elements, it divides the 8-element group G into 2 parts:

{(1),(1234),(13)(24),(1432)} = H and
{(24), (12)(34),(13), (14)(23)} (the rest).

If I were grading this, I would accept what I've written here as a decent proof although I might like references to theorems for each of the sentences which I just stated.

Hope that helps.

Lynn

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