1. 1.5 Literal Equations and Formulas ©2001 by R. Villar All Rights Reserved

2. Literal Equations and Formulas Literal Equation: Equation with more than one variable 3x + 2y = 6 This equation can be solved for either x or y. (We will be told which one to solve for). Here are other Literal Equations that you may have seen before:P = 2L + 2W d = rt A = 1 bh 2 You can solve for any of the variables in any of these equations. What is a Literal Equation?

3. The formula for the Perimeter of a Rectangle is P = 2L + 2W Example: Solve for W P = 2L + 2W – 2L –2L P – 2L = 2W P – 2L = 2W 2 2 P – 2L = W 2 How do I solve a literal equation, such as the formula for the perimeter of a rectangle, for one of its variables?

4. Example: Solve for P A = P + Prt Since P is in two terms, we’re going to need to factor it out (think Greatest Common Factor) in order to isolate it. A = P (1 + rt) Now, isolate P by dividing both sides by (1 + rt) P = A 1 + rt A = P (1 + rt) (1 + rt) How do I solve a literal equation for one variable when that variable is distributed in more than one term?

5. From Geometry, here’s the formula for the Volume of a cylinder: V = πr 2 h Example: Use the formula above to solve for h. V = πr 2 h πr 2 πr 2 h = V πr 2 r h

6. Here is the formula to find the area of an ellipse:A = πab Example: Find a if A = 65, b = 4 A = πab πb πb a = A a = 65 πb (3.14)(4) a ≈ 5.18 b a a b How do I manipulate the formula for the area of an ellipse, to solve for an unknown half length?