Question

Suppose that S varies directly as the ( 3)/(5) power of T, and that S=32 when T=32. Find S when T=243.

Answer 1

To solve for S when T = 243, you can use the formula for direct variation. First, find the constant of variation by substituting the given values into the equation. Then, plug in the given value of T to find the corresponding value of S.

Step-by-step explanation:

Solution

To solve for S, we can use the formula for direct variation:

S = k * T^(3/5)

First, we need to find the constant of variation, k. We can do this by substituting the given values into the equation:

32 = k * 32^(3/5)

Simplify the equation:

1 = k * 2^(3/5)

Divide both sides by 2^(3/5):

k = 1 / 2^(3/5)

Now that we know k, we can find S when T = 243:

S = (1 / 2^(3/5)) * 243^(3/5)

Calculate S using a calculator:

S ≈ 10.78

So, when T = 243, the value of S is approximately 10.78.