Write an equation that expresses each relationship. Then solve...

Question

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 root of w.

Accepted Answer

welcome back. I am so glad you're here. We are given this relationship, we're told that X varies jointly as Y. And the square of Z and X varies inversely as the square root of T. And first we are to start by writing this as an expression we recall from previous lessons that when we have variation that variable that varies. So in this case X is going to go on the left hand side of the equal sign and it's going to equal K. The constant term. And now when it varies jointly, then K is going to get multiplied by the variables that vary jointly. So K is going to get multiplied by why? And the square of Z. So K times Y. And the square of Z is Z squared. Alright. And when we have X varying inversely, then the inverse variation is going to go in the denominator below that K. So it varies inversely as the square root of T. That goes down here in the denominator. And now we've got that expression written out and we are to solve this equation for Z. So we want to isolate that Z. Alright, let's start off by multiplying both sides by the square root of T. Getting rid of that denominator. So on the left will have X. Square root of T. And on the right will have that equal to K. Y. Z squared. Alright. Getting Z by itself. Still let's divide both sides by ky And those kyi's will cancel out on the right hand side. So on the left we have X squared of T divided by K. Y. And that equals Z squared. We want to get rid of that squared. So we're going to take the square root of both sides. And on the right it will just be Z. So now we have Z equals which is what we wanted and it equals this convoluted thing, this square root of. And then in the numerator X square root again of T divided by K. Y. And we look at our answer choices in this matches with answer choice C. Well done, we'll catch you on the next one.

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 root of w.

Key Concepts

Joint Variation

Inverse Variation

Solving for a Variable in an Equation

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