In Exercises 45–47, solve each formula for the specified variable...

Question

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

Accepted Answer

Welcome back. I'm so glad you're here. We are solving this formula for M. Two. And we look at the formula and it's got M. Two on both sides and that M. Two on the right is inside that parentheses. And what we want to do is get it by itself on one side. So let's think about what we'll do here. We'll copy it down. M. Two V. One equals M. One plus M. Two times V. Two. Okay. So we'll work on getting the two M. Two S together. But first we have to free the one on the right from the bones of the parentheses. So let's distribute that V. Two to both terms the M. One and M. Two. So we've got M. Two V one carrying that down equals and I'm going to keep these in alphabetical order just for ease. But um we've got M. One V two plus M. Two V two. It would be the same thing if the V. Was first but it's easier to keep track of this way. So now where are terms that we're looking for? Here's one M. Two and here's the other M. Two. Okay. Not on the same side yet but we can bring this term over just by subtracting it. So subtract our M. Two V. Two. What we do to one side? We do the other minus M two V. Two and now we write that as M two. V one minus M two. V two equals. And these two terms cancel out. So now we've just got M one V. Two on the right where our terms that we're trying to isolate there are M. Two S. And hey look at that. That is a common factor in both of those terms. So we can factor that M two right out front. And that leaves us inside the parentheses with V one minus V two equals copy down the right side M one V two. And cool, we've just got one M two term now. And how do we get that by itself? Well, we can divide by the thing that's being multiplied by divide both sides by V one minus V two. We did to the one side. We've got to do the other and on the left those cancel out and on the left now we've just got our friend M. Two and that's on the right M one V two over parentheses V one minus V. Two. And look at that. We look at our answer choices very carefully and that's going to match with answer choice. D. Well done. We'll catch you on the next one

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