P varies directly as the square of Q and inversely as the cube of Z when P=5,Q=3 and Z=1
Find the relationship between P,Q,Z
Find Z when P=3 and Q=5
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
To find the relationship between P, Q, and Z, we can write the equation in a mathematical form based on the given information.
We are told that P varies directly as the square of Q and inversely as the cube of Z. This can be written as:
P ∝ Q^2 / Z^3
Now, let's find the constant of proportionality. We can do this by substituting the given values for P, Q, and Z and solving for the constant:
5 = k * (3^2) / (1^3)
5 = 9k
k = 5 / 9
Now that we have the value of k, we can write the relationship between P, Q, and Z:
P = (5 / 9) * (Q^2) / (Z^3)
To find Z when P = 3 and Q = 5, we can plug these values into the equation and solve for Z:
3 = (5 / 9) * (5^2) / (Z^3)
3 = 25 / (9Z^3)
9Z^3 = 25 / 3
Z^3 = 25 / (3 * 9)
Z^3 = 25 / 27
Taking the cube root of both sides, we get:
Z = ∛(25 / 27)
Z ≈ 0.925