Math Test Help

mathfreak101

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May 30, 2005
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My math test is tommorrow and I know there's a question like this on the test (from my math book).

The bed of a pond can be modeled by 25y = 2x^2 - 20x + 1, where x and y are measured in meters and the x-axis matches the water level of the pond. What is the width of the pond?

(HINT: This was in "Solving Quadratic Equations by Completing the Square" section) :wink:
 
mathfreak101 said:
The bed of a pond can be modeled by 25y = 2x^2 - 20x + 1, where x and y are measured in meters and the x-axis matches the water level of the pond. What is the width of the pond?
(HINT: This was in "Solving Quadratic Equations by Completing the Square" section) :wink:
OK, this took me a minute. What we have is a cross-sectional view of the pond. This makes the zero of the equation the shoreline on each side.

25y = 2x^2 - 20x + 1

If one were to use the "HINT", I suppose we should "complete the square" AT Y = 0

25(0) = 2x^2 - 20x + 1

Simplifying
0 = 2x^2 - 20x + 1

Divide by 2
0 = x^2 - 10x + 1/2

Complete the square (10/2 = 5 and 5^2 = 25)
0 = x^2 - 10x + 25 - 25 + 1/2

Rewrite
0 = (x-5)^2 - 49/2

Solve by factoring the difference of sqaures.
(x-5) + 7/sqrt(2) = 0 or (x-5) - 7/sqrt(2) = 0

You do the rest. Subtract the two solutions and you have the width for that cross section.
 
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