Question

Find the constant of variation for the relation and use it to write and solve the equation.

Answer 1

Answer:

When x = 1 and z = 4,   $y=\frac{80}{9}$

Step-by-step explanation:

The variation described in the problem can be written using a constant of proportionality "b" as:

$y=b\,\,x\,\,z^2$

The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":

$y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}$

Knowing this constant, we can find the value of y when x=1 and z=4 as:

$y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}$