In Exercises 11–20, write an equation that expresses each relatio...

Question

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies directly as the cube of z and inversely as y.

Accepted Answer

Welcome back. I am so glad you're here. We are given this relationship, we're told that X varies inversely as the square root of why and x varies directly as the So when we have got variation, we recall from previous lessons that the variable that varies is going to go on the left hand side of the equal sign. It's going to equal K. The constant term and the constant term K will be divided by anything that varies inversely. So it will be divided by the square root of why. And for direct variation, the constant term K will be multiplied by a variable that varies directly, so it will be multiplied by Z. So we have got that expression set up and now we are to solve the equation for Y. Let's start off by getting the square root of y out of the denominator and will multiply both sides by the square root of Y. So the left hand side will now be X. Square root of Y equals. And on the right hand side it'll just be K. Z. We're still trying to get Y by itself. So let's divide both sides by X. And the left hand side will just be the square root of Y. And the right hand side will be K times Z divided by X. Now to get Y by itself, we want to get rid of that square root. So we will square both sides. So the square root of Y squared will just be why? So we have Y equals which is what we wanted. And now to square each of those terms on the right hand side will have K squared times Z squared over X squared. We look at our answer choices and this matches with answer choice. A well done, we'll catch you on the next one.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube of z and inversely as y.

Key Concepts

Direct Variation

Inverse Variation

Combining Direct and Inverse Variation

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