Given the following relationship: answer each of the following questions. (optio

Question

Given the following relationship:

answer each of the following questions.
(options: 1/4 1/2 sqrt(1/2) 1 sqrt(2) 2 4 ) If A is cut in half while B and C are held constant, the new value of X will be ____ times the original value.

(options:1/4 1/2 sqrt(1/2) 1 sqrt(2) 2 4) If C is cut in half while A and B are held constant, the new value of X will be ____ times the original value.

(options: 1/4 1/2 sqrt(1/2) 1 sqrt(2) 2 4) If B is quadrupled while A and C are held constant, the new value of X will be ____ times the original value.

Explanation / Answer

if the given X = (A*sqrt(B)) / C

then  

If A is cut in half while B and C are held constant, the new value of X will be ____ times the original value.

let A2 = (1/2)A , B2 = B, C2 = C

then X2 = (A/2)sqrt(B)/C = (1/2)(A*sqrt(B))/C = 1/2*X

X2 = 1/2 *X

so the answer is option 1/2

----
If C is cut in half while A and B are held constant, the new value of X will be ____ times the original value.

A2 = (A) , B2 = B, C2 = C/2

then X2 = (A)sqrt(B)/(C/2) = (2)(A*sqrt(B))/C = 2*X

X2 = 2 *X

so the answer is option 2
-----------

If B is quadrupled while A and C are held constant, the new value of X will be ____ times the original value.

A2 = (A) , B2 = 4B, C2 = C

then X2 = (A)sqrt(4B)/(C) = (2)(A*sqrt(B))/C = 2*X

X2 = 2 *X

so the answer is option 2

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