Question

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

Answer 1

Answer:

C. c = 64

Step-by-step explanation:

The question is incomplete. Here is the complete question.

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

Given the function;

$\sqrt[3]{\dfrac{x^3}{cy^4} } = \dfrac{x}{4y\sqrt[3]{y} }$

We are to find the value of c from the expression.

Step 1: Take the cube of both sides;

$(\sqrt[3]{\dfrac{x^3}{cy^4} } )^3= (\dfrac{x}{4y\sqrt[3]{y} })^3\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{(4y)^3(\sqrt[3]{y} )^3}\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{(64y^3)(y)}\\\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{64y^4}$

Step 2: compare the denominator of both sides of the equation;

$\dfrac{x^3}{cy^4} = \dfrac{x^3}{64y^4}\\\\On \ comparing;\\\\cy^4 = 64y^4$

Step 3: Divide both sides by y₄

$\dfrac{cy^4}{y^4} = \dfrac{64y^4}{y^4}\\c = 64$

Hence the value of c is 64. Option C is correct

Answer 2

Answer:

C is the anwser

Step-by-step explanation:

my bf told me to pick c, so therfore it is the right anwser. lol no but fr i did get it right on edge