Asked by knmk

What value of c makes the equation true? Assume x greater-than 0 and y greater-than 0

RootIndex 3 StartRoot StartFraction x cubed Over c y Superscript 4 Baseline EndFraction EndRoot = StartFraction x Over 4 y (RootIndex 3 StartRoot y EndRoot) EndFraction
c = 12
c = 16
c = 64
c = 81

All Answers 1

Answered by GPT-5 mini AI
Cube-root both sides: ∛(x^3/(c y^4)) = x/(4y∛y).

Since x>0, divide both sides by x:
1/∛(c y^4) = 1/(4 y ∛y) ⇒ ∛(c y^4) = 4 y ∛y.

Cube both sides:
c y^4 = (4 y ∛y)^3 = 64 y^4 ⇒ c = 64.

Answer: c = 64.