This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Establish the relationship between P, Q, and R. The problem states that P varies directly as Q and inversely as the square root of R. This can be written as: P = (kQ)/(sqrt(R)) where k is the constant of proportionality. Step 2: Express the changes in Q and R. Let the initial values be P_1, Q_1, R_1. Q decreases by 4%, so the new value of Q, Q_2, is: Q_2 = Q_1 - 0.04 Q_1 = 0.96 Q_1 R increases by 44%, so the new value of R, R_2, is: R_2 = R_1 + 0.44 R_1 = 1.44 R_1 Step 3: Calculate the new value of P, P_2. Using the relationship from Step 1 with the new values Q_2 and R_2: P_2 = (kQ_2)/(sqrt(R_2)) Substitute the expressions for Q_2 and R_2: P_2 = (k(0.96 Q_1))/(sqrt(1.44 R_1)) P_2 = (k(0.96 Q_1))/(1.2 sqrt(R_1)) Rearrange the terms to relate P_2 to P_1: P_2 = ((0.96)/(1.2)) ((kQ_1)/(sqrt(R_1))) Since P_1 = (kQ_1)/(sqrt(R_1)), we have: P_2 = 0.8 P_1 Step 4: Calculate the percentage decrease in P. The percentage decrease is given by the formula: Percentage Decrease = (P_1 - P_2)/(P_1) × 100\% Substitute P_2 = 0.8 P_1: Percentage Decrease = (P_1 - 0.8 P_1)/(P_1) × 100\% Percentage Decrease = (0.2 P_1)/(P_1) × 100\% Percentage Decrease = 0.2 × 100\% Percentage Decrease = 20\% The percentage decrease in P is 20%. 20\% 3 done, 2 left today. You're making progress.