A rancher is going to fence three sides of a corral next to a river. He needs to maximize the corral area using 240 feet of fencing. The quadratic equation A (x) = x (240-20x) gives the area of the corral, A, for the length, x, of the corral along the river. Find the length of the corral along the river that will give the maximum area, and then find the maximum area of the corral.

Question

Mathematics

Kolby Simpson

4 September, 06:25

A rancher is going to fence three sides of a corral next to a river. He needs to maximize the corral area using 240 feet of fencing. The quadratic equation A (x) = x (240-20x) gives the area of the corral, A, for the length, x, of the corral along the river. Find the length of the corral along the river that will give the maximum area, and then find the maximum area of the corral.

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Answers (1)

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Azul Dixon · Answer 1

6 feet

Step-by-step explanation:

Actually we have to find the x value which corresponds to function

A (x) = x (240-20x) Function A9x) = x (240-20x) is quadratic and has 2 zeroes

To do that we have to find the function's zeroes x1 and x2:

x (240-20x) = 0

x1=0; 240-20x=0=> 20x=240=> x2=12

x value which corresponds to function's max is (x1+x2) / 2 = (0+12) / 2=6