Question

Suppose that w varies directly as the product of x and the square of y and inersely as z. when x = 2, y = 3, and z = 36, the value of w is 1/2. find the value of w when x = 5, y = 5, and z = 10.

Answer 1

The value of w is 12.5 when x = 5 , y= 5  and z = 10.

What is Equation of variation?

• A variation is a relation between a set of values of one variable and a set of values of other variables.
• In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

Equation of variation w = $\frac{kxy^{2} }{z}$

Constant of variation  k = $\frac{wz}{xy^{2} }$

Find k when w = 1/2, x = 2 and z = 36

k = $\frac{wz}{xy^{2} }$

$k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }$

$k = \frac{18}{2 * 9}$

$k = \frac{18}{18}$

k= 1

find the value of w when x = 5 , y = 5 and z = 10

$w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}$

$w = \frac{5^{3} }{10}$

w = 125 /10

w = 25 /2

w = 12 . 5

Therefore, the value of w is 12.5 when x = 5 , y= 5  and z = 10

Learn more about Equation of variation

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