Exam 6: Equations and Formulas

Use the formula $\frac { 1 } { C } = \frac { 1 } { C _ { 1 } } + \frac { 1 } { C _ { 2 } } + \frac { 1 } { C _ { 3 } }$ . Given $C _ { 1 } = 6.45 \times 10 ^ { - 7 } F$ , $C _ { 2 } = 5.25 \times 10 ^ { - 6 } F$ and $C _ { 3 } = 1.29 \times 10 ^ { - 8 } \mathrm {~F}$ . Find C.

Solve the formula for the given letter. $V = l w h \text { for } l$

Solve the formula for the given letter. $F = m a \text { for } m$

The equivalent resistance R of two resistances connected in parallel is given by $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Find the equivalent resistance for two resistances of 50 ? and 30 ? connected in parallel.

Solve the equation and check. $15 a - 14 ( a - 2 ) = 9$ a = __________

Solve this equation. $\frac { 3 } { 4 } v - \frac { 4 } { 3 } = - \frac { 7 } { 12 }$

Solve the equation and check. 3x - 10 = 5x - 20

Nick receives loans totaling $3,600 from two banks. One bank charges 7% annual interest, and the second bank charges 12% annual interest. He paid $307 in total interest in one year. How much was loaned at each bank?

Use the formula $\frac { 1 } { f } = \frac { 1 } { s _ { 0 } } + \frac { 1 } { s _ { i } }$ . Given f = 13.5 cm and $s 0$ = 25.5 cm, find $S _ { i }$ .

Solve the equation and check. $1 - \frac { 3 } { x } = \frac { 9 } { 5 x } - \frac { 3 } { 5 }$

Solve the equation and check. $2 ( 5 m - 6 ) - 9 = - 3$

Solve the equation and check. $\frac { 5 } { x } = 4$

Solve the formula for the given letter. $A = b h \text { for } h$

Solve the equation and check. $2 m = 77.4$

Solve the equation and check. $\frac { 7 } { x } = 6$

Solve the formula for the given letter. $I = \frac { Q } { t } \text { for } t$

Solve the formula for the given letter. $R = \frac { \rho L } { A } \text { for } L$

One side of a rectangular yard is bounded by the side of a house. The other three sides are to be fenced with 81 ft of fencing. The length of fence opposite the house is 15 ft less than either of the other two sides. Find its length and width.

Solve the formula for the given letter. $F = a b + \frac { d } { 2 } ( a + c ) \text { for }$

Solve the equation and check. $9 ( w - 1 ) = w + 7$ w = __________