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If t varies inversely as the cube of z and directly as the square of r, and t = 4 when z = 3 and r =6, find t when z = 6 and r = 9

Sagot :

If t varies inversely as the cube of z, the the equation relating t and z is expressed as

t = k/z^3

where

k is the proportionality constant

If t varies directly as the square of r, then the equation relating them is

t = kr^2

This is combined variation The formula relating all the variables would be

t = kr^2/z^3

From the information given,

t = 4, z = 3 and r = 6

By substituting these values into the formula,

4 = k * 6^2/3^3

4 = 36k/27 = 4k/3

By cross multiplying,

4 * 3 = 4k

k = (4 * 3)/4

k = 3

Thus, the formula is

t = 3r^2/z^3

When z = 6 and r = 9, we have

t = 3 * 9^2/6^3

t = 243/216

t = 1.125

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