In Exercises 45–46, describe in words the variation shown by the ...

Question

In Exercises 45–46, describe in words the variation shown by the given equation.

z = kx^2 √y

Accepted Answer

Welcome back. I am so glad you're here. We are given this equation the equals K times the square root of X, times Y cubed. And were asked to explain this relationship in words, well, we notice that we have the constant term K here and when we have the constant term K, we're dealing with variation. When we describe variation, we start reading the left hand side of the equation. So in this case we start with Z. And we say that Z varies and then after that it really depends on what is happening to the K constant term. It can be varying either directly or inversely and we decide if it's direct or inverse by seeing if these other terms are being multiplied by the K or if the K is being divided by the other terms. If K is being multiplied, it is direct variation. If K is being divided, it is inverse variation. And in this case K is being multiplied by both terms the square root of X and Y cubed. So we look at our answer choices and this matches answer choice. A. Z varies directly as the square root of X and the cube of why. Well done. We'll catch you on the next one.

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In Exercises 45–46, describe in words the variation shown by the given equation. z = kx^2 √y