Use the four-step procedure for solving variation problems given ...

Question

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Accepted Answer

Welcome back. I am so glad you're here. We are given this multi step problem here. We're told that Q varies jointly as P and R. Alright, we recall from previous lessons on variation that that variable that varies goes on the left hand side of the equation. So Q equals and it's going to equal the constant term K. And when we have joint variation, the variables that vary jointly. So in this case P and r are going to get multiplied by the constant term K. And cue also varies inversely as the square root of S. When we have inverse variation, then the K. Is going to be divided by the variable that varies inversely. So it is K times P times are divided by the square root of S. So we've set up that problem and we're told a couple of different things. We're told That q equals 24 And we're told that P equals 12. We're told that r equals eight And we're told that s equals 36. We are to find Q. Where P I'm gonna copy over that K. So where P equals one, Where our equals And where s. equals four. So in order to solve this equation over here on the right hand side for Q. We first need to figure out what that constant term K. Is. And we can solve that. Using the equation on the left we have every variable there except for K. So now we just need to do the math on the left 12 times eight in the numerator will give us a 96 K divided by the squared of 36 is six, that equals 24 so divided by six is going to be 16. So we've got 16 K on the right hand side and that equals 24. We can divide both sides by 16 and we get K equals three halves or 1.5. So we can now substitute this K. This three halves and for our K. In this equation and we can just do all that multiplication and division on the right hand side to solve for Q. So three halves times one times 28 that equals 42 divided by the square root of four. That is to So q equals 42 divided by two or 21. There is our solution. We look at our answer choices and this matches with answer choice. A Well done. We'll catch you on the next one.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Key Concepts

Joint Variation

Inverse Variation

Four-Step Problem Solving Procedure

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