Chapter 3.8, Problem 8CFU

To determine

To find: The constant of variation for given relation and use it to write an equation for given statement. Then solve the equation.

If y varies jointly as x and z and inversely as the square of w and y = 3 when x = 3, z = 10 and w = 2, find y when x = 4, z = 20 and w = 4.

Answer to Problem 8CFU

  $y=4$

Explanation of Solution

Given information: If y varies jointly as x and z and inversely as the square of w and y = 3 when x = 3, z = 10 and w = 2, find y when x = 4, z = 20 and w = 4.

Calculation:

Since y varies jointly asx andz and inversely as the square of w. Then,

  $y=\frac{kxz}{w^2}$

Use the given initial information to find k.

The new equation then is:

  $\begin{array}{l}y=\frac{xz}{5w}\\ 3=\frac{k\left(3\right)\left(10\right)}{2}\to k=\frac{1}{5}\end{array}$

Substitute the given information to find y.

  $\begin{array}{l}y=\frac{\left(4\right)\left(20\right)}{5\left(4\right)}\\ y=4\end{array}$