If f (x) varies directly with x2, and f (x) = 40 when x = 2, find the value of f (5).

A. 100

B. 50

C. 250

D. 25

C. 250

Step-by-step explanation:

If f (x) varies directly with x^2

f (x) = k * x^2

f (x) = 40 when x=2. Substitute these values in

40 = k (2) ^2

40 = k*4

Divide by 4

40/4 = 4k/4

10 = k

f (x) = 10x^2

Now we want to find f (x) when x=5. Substituting

f (5) = 10 * 5^2

f (5) = 10 * 25

f (5) = 250