Question

isolate for the intended variable in the following equations.

1. in the distance formula, ( d = rt ), solve for ( t ).

1. in the formula for the perimeter of a circle, ( c = 2pi r ), solve for ( r ).

1. in the formula for the area of a triangle, ( a = \frac{1}{2} bh ), solve for ( b ).

1. in the formula for the area of a circle, ( a = pi r^2 ), solve for ( r ).

Explanation:

Step1: Solve \(d = rt\) for \(t\)

Divide both sides by \(r\): \(t = \frac{d}{r}\)

Step2: Solve \(C = 2\pi r\) for \(r\)

Divide both sides by \(2\pi\): \(r = \frac{C}{2\pi}\)

Step3: Solve \(A = \frac{1}{2}bh\) for \(b\)

Multiply by 2 then divide by \(h\): \(b = \frac{2A}{h}\)

Step4: Solve \(A = \pi r^2\) for \(r\)

Divide by \(\pi\) then take square root: \(r = \sqrt{\frac{A}{\pi}}\)

Answer:

1. \(t = \frac{d}{r}\)
2. \(r = \frac{C}{2\pi}\)
3. \(b = \frac{2A}{h}\)
4. \(r = \sqrt{\frac{A}{\pi}}\)