P varies directly as the square of Q and inversely as the square root of R. If Q is reduced by 12% and R is reduced by 21%, find the percentage change in P

Answer 1

Let P1, Q1, and R1 be the original values of P, Q, and R, respectively.
Let P2, Q2, and R2 be the new values of P, Q, and R, respectively.

According to the problem, we have the following relationships:
P1 ∝ Q1^2 (P is directly proportional to the square of Q)
P1 ∝ 1/√R1 (P is inversely proportional to the square root of R)

Combining the two relationships, we have:
P1 ∝ Q1^2 / √R1

Now, let's consider the changes in Q and R. Q is reduced by 12%, so Q2 = 0.88Q1.
R is reduced by 21%, so R2 = 0.79R1.

Substituting these new values into the relationship, we have:
P2 ∝ (0.88Q1)^2 / √(0.79R1)

Simplifying, we get:
P2 ∝ 0.7744Q1^2 / √R1

To find the percentage change in P, we compare P2 and P1:
Percentage change = ((P2 - P1) / P1) * 100
= ((0.7744Q1^2 / √R1 - P1) / P1) * 100

However, we don't have enough information to calculate the exact percentage change in P because the values of Q1 and R1 are not given.