Question

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5. What is the value of Z when X=8, and Y= 12

Round to at least thee thousandths place if needed.

**************PLEASE HELP**************************

Answer 1

Directly proportional to x

z=kx

And inversely proportional to y

z=kx/y we are given the point (x,y,z) of (3, 6, 9.5) so

9.5=3k/6 now multiply both sides by 6

57=3k divide both sides by 3

19=k so now that we know the constant of proportionality:

z=19x/y, and we want to solve for z when x=8 and y=12 so:

z=19(8)/12

z=12 2/3 exact

z≈12.667 (rounded to the nearest thousandth)