P varies directly as the square of Q and inversely as the cube of Z when P=5,Q=3 and Z=1

Question

Find the relationship between P,Q,Z
Find Z when P=3 and Q=5

Answer 1

The relationship between P, Q, and Z can be expressed as:

P ∝ Q^2/Z^3

To find Z when P=3 and Q=5, we can rearrange the formula to solve for Z:

P ∝ Q^2/Z^3
Z^3 ∝ Q^2/P
Z^3 ∝ 5^2/3
Z^3 ∝ 25/3
Z^3 ∝ 8.33

To find Z, we can take the cube root of 8.33:

Z ≈ ∛8.33
Z ≈ 2.04