find an equation

Question

Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7

the equation of varation is y= ???????

Answer 1

When you say Y varies jointly with respect to z^2 and x you are saying that for some number K,

Y= Kxz^2.

A point for Y, x and z was given so all that needs to be done is to solve for the single unknown and you have the answer for the equation of variation.

231=K6(7^2) ---------> 231=6*49*K ------------> 231=K*294 --------> 231/294=K.

Simplify to get K = 11/14

Thus the equation of variation is $Y=\frac{11}{14}\cdot x\cdot z^2$