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

Question

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

Accepted Answer

Welcome back. I'm so glad you're here. We are solving for the variable D. In this formula here. So where's the D. There's a D squared on the right side, so we want to get that D all by itself without any other variables anywhere else around it. So we'll rewrite it quick. I sub P equals I sub C. M plus M times D squared. And we're going to do like the opposite of AARP mds where parentheses exponents multiplication, divide addition and subtraction. And we're going to move everything away from the D. By starting with adding and subtracting the I. C. M. Is being added to the M. D. Squared. So that's gonna be the easiest one to get rid of to undo that positive. I see. Em we're going to subtract it from both sides and subtract I sub cm. And on the left it's not going to read I C P minus I sub C. M. Equals. And these will cancel out. So we've got M. D squared on the right, we're trying to get that D. By itself. And now it's being multiplied by the M. That's the next thing. And to undo that multiplication, we will divide both sides by the M. And so on the left side we've got I sub P minus I sub C. M over M equals those M's cancel out D squared. We've almost got D by itself. Now it's just being squared. And that's those exponents that we've got here to undo that squared. One thing we would normally do is take the square root of both sides. But if we look really quick over in our answers, there isn't anything that has a square root in it. So what's another way we can think about square roots? Well, a square root is the same as something raised to the one half power. So instead of taking the square root we are going to say I sub p minus I subsea um over em all raised to the one half power and we're going to take that D squared and raise that to the one half power. Because we'll multiply those exponents two times one half that equals one. So now it's D. To the first which is just D. And we finally do have that D. By itself will re rate I sub p minus I sub cm over em all raised to the one half equals D. Because these cancel out. And now we do have the D. Isolated. We look very carefully at our answer choices and it's going to match answer choice C. Well done. We'll catch you on the next one

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

Key Concepts

Algebraic Manipulation

Quadratic Equations

Isolating Variables

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