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 jointly as y and z and inversely as the square of w.

Accepted Answer

Welcome back. I am so glad you're here, we are Given this relationship, X varies jointly as Y and the square of Z and X varies inversely as the square of T. So were to write this as an expression we recall from previous lessons on variation that the term that varies is going to go on the left hand side of the equal sign and it will equal the constant term K. And now K. Because we have Y and the square of Z varying jointly. Why in the square Z will get multiplied by K. So K times Y and the square of Z. That's Z squared. And now X is going to vary inversely as the square of T. That means that the constant term K is going to be divided by the square of T, which is T squared. And now we are to solve this equation for T. So we want to get T by itself. Well, let's get T out of the denominator first of all, let's multiply both sides by T squared. And so on the left, we'll have X. T squared and on the right will have K, Y, Z squared. Now we want to get that T by itself. So let's divide both sides by X. Which will give us on the left, T squared. And on the right, K, Y Z squared over X. And the final step to get T by itself is we're going to take the square root of both sides. That square root of T squared will just give us a T and we'll have T equals. Now let's simplify a little bit. The only one we can take, The square root of is this Z squared. So the square root of Z squared is Z. That comes out in front and that's getting multiplied by everything that's left the square root of K. Y. In the numerator divided by X. We look at our answer choices and this matches with answer choice D. 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 jointly as y and z and inversely as the square of w.

Key Concepts

Joint Variation

Inverse Variation

Solving for y

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