In Exercises 35–54, solve each formula for the specified variable...

Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

1/R = 1/R1 + 1/R2 for R1

Accepted Answer

welcome back. I'm so glad you're here. We have got a formula, I'll write it a bit bigger. We've got one divided by T equals one divided by T. Sub one plus one divided by T. Sub two. And we are to solve it for T. Sub two, meaning we want to get this T sub two all by itself on one side of the equal sign. So the first thing we'll do to get it by itself is we will subtract away this one divided by T. Sub one. What we do to one side we do to the other. So in effect we're bringing it to the left hand side of the equation. Now the left hand side looks like one divided by T minus one divided by T. Sub oh that's not a two, that should be a one. So T sub one equals and on the right hand side one divided by T. Sub two because these one divided by T. Sub ones, cancel each other out. Now to how to get that T sub two by itself, let's bring it out of the denominator, let's get rid of the fraction on the right hand side by multiplying it by T. Sub two. And what we do to one side we've got to do to the other. So multiply both sides by T. Sub two. On the right hand side, those types of twos cancel out. So the right hand side is just one and on the left hand side it's T sub two times one divided by T minus one divided by T. S of one. And we do not want to distribute that T. Sub two. We want to keep them factored like this because for our next step we can divide both sides by this factor one divided by t minus one, divided by T. S. Of one. What we do to one side we do to the other. Oops that's too big one, divided by t minus one, divided by T. S. Of one. And on the left hand side those factors cancel out. And we just have T. Sub two which is exactly what we were looking for. The right hand side has one divided by one divided by t minus one divided by T. Sub one. And that will match our answer choice. D Now if you're looking for the bonus answer, are you familiar with the formula? What does it represent? Well this original formula here is the formula for work problems that involve hours that involve time. So let's say we were talking about painting a house and Susie paints the house in two hours. So Susie's time would be T sub one equals two. And let's say that Frieda paints the house in five hours. So she'd be T sub two equals five. And then t would be how long it takes them together. So you go one divided by two plus one divided by five replacing our T sub one and artists up to and that equals one over T. And at that point you just solve for t to find out how long it took them to do it together. Well, well done, we'll catch you on the next one.

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