Final answer:
To solve the equation (y-5)³-64=0, add 64 to both sides, take the cube root, and solve for y. The value of y is 9.
Step-by-step explanation:
To solve the equation (y-5)³ -64=0, we need to find the value of y that satisfies the equation.
1: Add 64 to both sides of the equation to isolate the term with y.
(y-5)³ = 64
2: Take the cube root of both sides to undo the exponent.
Cube root of (y-5)³ = cube root of 64
y-5 = 4
3: Add 5 to both sides to solve for y.
y = 9
Therefore, the value of y that satisfies the equation is 9.