Question

Y varies jointly as x and z, and inversely as w: y=3 when x=-2, z=6, and w=12.

•Write the equation that represents this relationship.
•What is the constant?

Answer 1

Write the equation that represents this relationship

$y = -3 \times \frac{xz}{w}$

The constant is -3

Solution:

Given that,

y varies jointly as x and z, and inversely as w

Therefore,

$y \propto \frac{xz}{w}$

$y = k \times \frac{xz}{w} ------ eqn\ 1$

Where, k is constant of propotionality

y = 3 when x = -2, z = 6, and w = 12

Substitute in eqn 1

$3 = k \times \frac{-2 \times 6}{12}\\\\3 = k \times -1\\\\k = -3$

Write the equation that represents this relationship

Substitute k = -3 in eqn 1

$y = -3 \times \frac{xz}{w}$

Thus the equation is found