SAT Math : Direct and Inverse Variation

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #3 : How To Use The Inverse Variation Formula

varies directly as the square of and the cube root of , and inversely as the fourth root of . Which of the following is a true statement?

Possible Answers:

varies directly as the square root of and the eighth root of , and inversely as the sixth power of .

varies directly as the square root of and the eighth root of , and inversely as the sixth root of .

varies directly as the square root of and the eighth power of , and inversely as the sixth root of .

varies directly as the square root of , and inversely as the eighth root of and the sixth root of .

 varies directly as the square root of , and inversely as the eighth power of  and the sixth power of .

Correct answer:

varies directly as the square root of and the eighth root of , and inversely as the sixth root of .

Explanation:

varies directly as the square of and the cube root of , and inversely as the fourth root of , so, for some constant of variation ,

We take the reciprocal of both sides, then extract the square root:

Taking as the constant of variation, we see that varies directly as the square root of and the eighth root of , and inversely as the sixth root of .

Example Question #11 : Direct And Inverse Variation

If  varies inversely as , and  when , find  when .

Possible Answers:

Correct answer:

Explanation:

The formula for inverse variation is as follows: 

Use the x and y values from the first part of the sentence to find k. 

Then use that k value and the given x value to find y.

 

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