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
Let's solve this problem step-by-step. Step 1: Write the proportionality relationship. If X is directly proportional to the square of Y, we can write: X = kY² where k is the constant of proportionality. Step 2: Define the original and new values of Y. Let the original value of Y be Y₁. Y₁ = Y Y increases by 20%, so the new value of Y, Y₂, is: Y₂ = Y₁ + 0.20Y₁ Y₂ = 1.20Y₁ Step 3: Calculate the original and new values of X. Original X, X₁: X₁ = kY₁² New X, X₂: Substitute Y₂ into the proportionality equation: X₂ = k(Y₂)² X₂ = k(1.20Y₁)² X₂ = k(1.44Y₁²) X₂ = 1.44(kY₁²) Since X₁ = kY₁², we can write: X₂ = 1.44X₁ Step 4: Calculate the percentage change in X. The formula for percentage change is: Percentage Change = ((New Value - Original Value) / Original Value) × 100% Percentage Change in X = ((X₂ - X₁) / X₁) × 100% Substitute X₂ = 1.44X₁: Percentage Change in X = ((1.44X₁ - X₁) / X₁) × 100% Percentage Change in X = (0.44X₁ / X₁) × 100% Percentage Change in X = 0.44 × 100% Percentage Change in X = 44% The percentage change in X is an increase of 44%. Send me the next one 📸