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?

S = P + Prt for r

Accepted Answer

Welcome back. I'm so glad you're here. We've got this formula. It is a sub N equals a sub one plus parentheses and minus one times D. And we are solving for D. Meaning we want to get D by itself on one side of the equal sign. Well how do we do that? We have to move over all the rest of this stuff. And in what order do we move that? Well we actually now want to recall the order of operations, parentheses, exponents, multiplication and division and then addition and subtraction. And we normally start with parentheses and work our way to the right to move things away from the D. We're actually going to start on the right with addition and subtraction and work our way to the left. We want to start with the things farthest removed from that D. In the farthest removed one here in this case there is addition happening with that a sub one and we're going to do the opposite of addition to bring that over to the other side. So that is positive and we're going to subtract a sub one and what we do to one side we need to do to the other. And now on the right hand side that a sub one minus a sub one. Well now that's zero and that's how we've gotten rid of it on the right hand side. And the left hand side now reads a sub n minus a sub one equals and the right hand side is parentheses and minus one times D. Now the only operation left happening with the D. On the right hand side is multiplication. So we've gotten the addition and subtraction done and now we're doing multiplication and division. And so the D. A. Is being multiplied by the end minus one. And we need to undo that by doing the opposite. So the opposite of multiplication is division. We're going to divide by n minus one and what we do to one side we need to do to the other. And because what happens on the right hand side N minus one divided by n minus one. Will those cancel out those factors cancel out now? That's just one or one times D. And one times D. Well that's just D. Which is exactly what we wanted. The D. Is now by itself and we just copy that left hand side a sub n minus a sub one, divided by n minus one. And that is getting the D indicated variable all by itself. We've solved for it and we look at our answer choices and that matches answer choice C. This formula happens to be the 10th term of an arithmetic sequence. While done. We'll catch you on the next one

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