If y varies directly as the square of x and inversely as the cube root of z, where y = 9 when x = 3 and z = 8, find the equation of variation.

Question

Accepted Answer

Step:1 ：Step 1: Since y varies directly as the square of x and inversely as the cube root of z, we can express this as ( y = k frac{x^2}{{z^{1/3}}} ) where k is a constant.Step:2 ：Step 2: Substitute y = 9, x = 3, z = 8 into the equation to find the constant k. So, ( 9 = k frac{3^2}{{8^{1/3}}} )Step:3 ：Step 3: Solve the equation for k. We find ( k = 9 times frac{{8^{1/3}}}{9} = 8^{1/3} )Step:4 ：Step 4: Substituting k back into the equation, we get ( y = 8^{1/3} frac{x^2}{{z^{1/3}}} )

Answer

Step: 1 ：Step 1: Since y varies directly as the square of x and inversely as the cube root of z, we can express this as ( y = k frac{x^2}{{z^{1/3}}} ) where k is a constant.Step: 2 ：Step 2: Substitute y = 9, x = 3, z = 8 into the equation to find the constant k. So, ( 9 = k frac{3^2}{{8^{1/3}}} )Step: 3 ：Step 3: Solve the equation for k. We find ( k = 9 times frac{{8^{1/3}}}{9} = 8^{1/3} )Step: 4 ：Step 4: Substituting k back into the equation, we get ( y = 8^{1/3} frac{x^2}{{z^{1/3}}} )

If y varies directly as the square of x and inversely as the cube root of z, where y = 9 when x = 3 and z = 8, find the equation of variation.

Answer

Popular Problems