Question

T varies directly as the square of d and inversely as f. If t =192 when d=8 and f=4, determine t when d=10 and f=6.

Answer 1

To solve this problem, we can use the formula for direct and inverse variation:
T = k(d^2/f)

where k is the constant of proportionality.

To find k, we can use the values given in the problem:
192 = k(8^2/4)

Simplifying this equation, we get:
192 = k(16)
k = 12

Now that we have k, we can use the formula to find t when d=10 and f=6:
T = 12(10^2/6)
T = 200

Therefore, when d=10 and f=6, the value of t is 200.