Question

Y varies directly as the square root of t and inversely as s. If y=12 when t=36 and s=2, determine y when t=81 and s=4.

Answer 1

To solve this problem, we can use the formula for direct and inverse variation, which states that:
y = k * sqrt(t) / s

where k is the constant of proportionality. We can find k by plugging in the values of y, t, and s from the first set of data:
12 = k * sqrt(36) / 2

Simplifying this equation, we get:
k = 4

Now that we know k, we can use the same formula to find y when t=81 and s=4:
y = 4 * sqrt(81) / 4
y = 9

Therefore, when t=81 and s=4, y is equal to 9.