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 variation equation. The problem states that X varies directly as the product of U and V, and inversely as their sum. This can be written as: X = k (UV)/(U+V) where k is the constant of proportionality. Step 2: Find the constant of proportionality, k. We are given that X = 3 when U = 3 and V = 1. Substitute these values into the equation: 3 = k (3 × 1)/(3 + 1) 3 = k (3)/(4) To solve for k, multiply both sides by (4)/(3): k = 3 × (4)/(3) k = 4 Step 3: Write the complete variation equation. Now that we have the value of k, the equation becomes: X = 4 (UV)/(U+V) Step 4: Calculate the value of X using the new values. We need to find X when U = 3 and V = 3. Substitute these values into the complete equation: X = 4 (3 × 3)/(3 + 3) X = 4 (9)/(6) Step 5: Simplify the expression for X. X = 4 × (3)/(2) X = 2 × 3 X = 6 That's 2 down. 3 left today — send the next one.