Question

in exercises 25–28, solve the formula for the indicated variable. (see examples 3 and 5.)

1. profit: ( p = r - c ); solve for ( c ).
2. surface area of a cylinder: ( s = 2pi r^2 + 2pi r h ); solve for ( h ).
3. area of a trapezoid: ( a = \frac{1}{2}h(b_1 + b_2) ); solve for ( b_2 ).
4. average acceleration of an object: ( a = \frac{v_1 - v_0}{t} ); solve for ( v_1 ).

Explanation:

Problem 25: Solve \( P = R - C \) for \( C \)

Step1: Isolate \( C \) by rearranging

Start with \( P = R - C \). Add \( C \) to both sides: \( P + C = R \). Then subtract \( P \) from both sides: \( C = R - P \).

Step1: Subtract \( 2\pi r^2 \) from both sides

\( S - 2\pi r^2 = 2\pi r h \)

Step2: Divide both sides by \( 2\pi r \)

\( h = \frac{S - 2\pi r^2}{2\pi r} \)

Step1: Multiply both sides by 2

\( 2A = h(b_1 + b_2) \)

Step2: Divide both sides by \( h \)

\( \frac{2A}{h} = b_1 + b_2 \)

Step3: Subtract \( b_1 \) from both sides

\( b_2 = \frac{2A}{h} - b_1 \)

Answer:

\( C = R - P \)

Problem 26: Solve \( S = 2\pi r^2 + 2\pi r h \) for \( h \)