Question

The function f(x)=x(200-x) models the area of a pasture, in square yards, as a function of its length. Which are possible lengths of the pasture? 125 yards 200 yards 170 yards 225 yards 210 yards

Answer 1

Answer:

(a): x = 125 yards.

(c): x = 170 yards.

Step-by-step explanation:

Given

$f(x) = x(200 - x)$

$x = length$

$f(x) = area$

Required

Determine the possible length

For a length to be possible or usable, the calculated area must be greater than 0.

(a): x = 125 yards.

$f(x) = x(200 - x)$

Substitute 125 for x

$f(125) = 125 * (200 - 125)$

$f(125) = 125 * 75$

$f(125) = 9375$

(b): x = 200 yards.

$f(x) = x(200 - x)$

Substitute 200 for x

$f(200) = 200 * (200 - 200)$

$f(200) = 200 * 0$

$f(200) = 0$

(c): x = 170 yards.

$f(x) = x(200 - x)$

Substitute 170 for x

$f(170) = 200 * (200 - 170)$

$f(170) = 200 * 30$

$f(170) = 6000$

(d): x = 225 yards.

$f(x) = x(200 - x)$

Substitute 225 for x

$f(225) = 200 * (200 - 225)$

$f(225) = 200 * (- 25)$

$f(225) = -5000$

(e): x = 210 yards.

$f(x) = x(200 - x)$

Substitute 210 for x

$f(220) = 200 * (200 - 210)$

$f(220) = 200 * (- 10)$

$f(220) = -2000$

From the above calculations, only values of x that are 125 and 170 makes the function true