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: Write the direct variation equation. If P varies directly as the square of Q, the relationship can be written as: P = kQ^2 where k is the constant of variation. Step 2: Find the constant of variation (k). We are given P=3 when Q=2. Substitute these values into the equation: 3 = k(2^2) 3 = k(4) To find k, divide both sides by 4: k = (3)/(4) Step 3: Find Q when P=27. Now use the constant k = (3)/(4) and the new value P=27 in the variation equation: 27 = (3)/(4)Q^2 To solve for Q^2, multiply both sides by (4)/(3): Q^2 = 27 × (4)/(3) Q^2 = 9 × 4 Q^2 = 36 Take the square root of both sides to find Q: Q = ±sqrt(36) Q = ± 6 The possible values for Q are 6 and -6. The final answer is Q = ± 6. Send me the next one 📸