The area A of a circle in terms of the circle's radius r is A= πr². a. Explain the restrictions on the domain of the function A = πr² and the inverse function in this context. b. Write the inverse function of A = πr². c. Use the inverse function you wrote in part (b) to find the radius of a circle that has an area of 50.25 in.². Round your answer to the nearest inch.

If the radius of a circle of area $A$ and circumference $C$ is doubled, find the new area and circumference of the circle in terms of $A$ and $C$.

Decide whether the function has an inverse function. If so, what is the inverse function? h(t) is the height of the tide t hours after midnight, where 0 ≤ t < 24.

Decide whether the function has an inverse function. If so, what is the inverse function? A(r) is the area of a circle of radius r.

The formula for converting kilometers to miles is m = 1.609k, where m is miles and k is kilometers. Transform this formula to find a formula for converting miles to kilometers. Use this formula to determine the number of kilometers in 539 miles and in 7380 miles, rounded to the nearest kilometer.

Decide whether the function has an inverse function. If so, what is the inverse function? g(t) is the volume of water that has passed through a water line t minutes after a control valve is opened.

Solve for x: 12 = 2x - 16.

Simplify each expression.

$$(bc)^5$$

Does the problem involve permutations or combinations? Explain your answer. (It is not necessary to solve the problem.) How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?

The height of a species of dwarf evergreen tree, in centimetres, as a function of time, in months, can be modelled by the logistic function $h(t)=\frac{275}{1+26(0.85)^{t}}$. a) If this function is graphed, are there any asymptotes? If so, name each asymptote and describe what it means. b) Determine when this tree will reach a height of 150 cm.

Solve. Use substitution to check. $- \frac { 3 } { 8 } b = - \frac { 1 } { 2 }$

A(n) ______ is an atom or group of atoms that replaces a hydrogen in a hydrocarbon molecule.

find the inclination θ (in radians and degrees) of the line. -2√3x - 2y = 0

$$\begin{array} { r } { 3 \frac { 1 } { 2 } } \\ { + \quad 1 \frac { 1 } { 3 } } \\ \hline \end{array}$$