Algebra Review: Literal Equations

Use With Lesson 11-2

A literal equation is an equation involving two or more variables. A formula is a special type of literal equation. You can transform a formula by solving for one variable in terms of the others.

Example

1. The formula for the volume of a cylinder is V = π r 2 h . v equals , pi . r squared , h . Find a formula for the height in terms of the radius and volume.

   V = π r 2 h Use the formula for the volume of a cylinder. V π r 2 = π r 2 h π r 2 Divide each side by  π r 2 , with  r ≠ 0 . V π r 2 = h Simplify. table with 3 rows and 3 columns , row1 column 1 , v equals , column 2 pi , r squared , h , column 3 table with 2 rows and 1 column , row1 column 1 , cap usetheformulaforthe , row2 column 1 , volumeofacylinder. , end table , row2 column 1 , fraction v , over pi , r squared end fraction . equals , column 2 fraction pi , r squared , h , over pi , r squared end fraction , column 3 table with 2 rows and 1 column , row1 column 1 , cap divideeachsideby . pi , r squared , comma , row2 column 1 , with . r not equal to 0 , . , end table , row3 column 1 , fraction v , over pi , r squared end fraction . equals , column 2 h , column 3 cap simplify. , end table

   The formula for the height is h = V π r 2 . h equals . fraction v , over pi , r squared end fraction . .

2. Find a formula for the area of a square in terms of its perimeter.

   P = 4 s Use the formula for the perimeter of a square. P 4 = s Solve for  s  in terms of  P . A = s 2 Use the formula for area. = ( p 4 ) 2 Substitute  P 4  for  s . = p 2 16 Simplify . table with 5 rows and 3 columns , row1 column 1 , p equals , column 2 4 s , column 3 table with 2 rows and 1 column , row1 column 1 , cap usetheformulaforthe , row2 column 1 , perimeterofasquare. , end table , row2 column 1 , p over 4 , equals , column 2 s , column 3 cap solvefor . s . intermsof p . , row3 column 1 , eh equals , column 2 s squared , column 3 cap usetheformulaforarea. , row4 column 1 , equals , column 2 open , p over 4 , close squared , column 3 cap substitute . p over 4 , for , s . , row5 column 1 , equals , column 2 fraction p squared , over 16 end fraction , column 3 cap simplify , . , end table

   The formula for the area is A = P 2 16 . eh equals , fraction p squared , over 16 end fraction , .

Exercises

Algebra Solve each equation for the variable in red.

1. C = 2 π r c equals 2 , pi r
2. A = 1 2 b h eh equals , 1 half , b h
3. A = π r 2 eh equals , pi , r squared

Algebra Solve for the variable in red. Then solve for the variable in blue.

4. P = 2 w + 2 l p equals . 2 w plus 2 l
5. tan   A = y x tangent eh equals , y over x
6. A = 1 2 ( b 1 + b 2 ) h eh equals , 1 half . open . b sub 1 , plus , b sub 2 . close . h

Find a formula as described below.

7. the circumference C of a circle in terms of its area A
8. the area A of an isosceles right triangle in terms of the hypotenuse h
9. the apothem a of a regular hexagon in terms of the area A of the hexagon
10. Solve A = 1 2 a b   sin C eh equals , 1 half , eh b sine c for m ∠ C . m angle c .

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