Activity 7 1. If x varies as the square of y and inversely as z and x = 12 when y = 3 and z = 6, find x when y = 9 and z = 6. 2. w varies directly as x and inversely as y and w = 120 when x = 4, y = 3. Find w when x = 1, y = 15.
Answer (1)
Problem 1:Given: x ∝ y²/z, x = 12 when y = 3, z = 6Equation: x = k(y²/z)Substitute given values: 12 = k(3²/6)12 = k(9/6)12 = k(1.5)Find k: k = 12/1.5k = 8Now, find x when y = 9, z = 6:x = 8(9²/6)x = 8(81/6)x = 8(13.5)x = 108Problem 2:Given: w ∝ x/y, w = 120 when x = 4, y = 3Equation: w = k(x/y)Substitute given values: 120 = k(4/3)120 = k(1.33)Find k: k = 120/1.33k ≈ 90.23Now, find w when x = 1, y = 15:w = 90.23(1/15)w ≈ 6.01The answers are:1. x = 1082. w ≈ 6.01
