The following assignment statements either contain at least one error, or could be improved in some way. Assume that radius is a variable that has been initialized. First, identify the problem, and then fix and/or improve them:

33 =number
my variable = 11. 11;
area = 3. 14 * radius ^2;
x = 2 * 3. 14 * radius;

True or False. The curvature $\kappa$ of a circle equals the radius of the circle.

A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increasing by 2 feet per second, how fast is the area changing when the radius is 10 feet?

The circumference of a circle is $8 \pi$ feet. Find the radius of the circle.

Identify the function’s local and absolute extreme values, if any, saying where they occur. $K(t)=15 t^{3}-t^{5}$

Find the series' radius and interval of convergence.

$$\sum_{n=1}^{\infty} n^n x^n$$

A car is traveling at 80 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy inter section. The car's velocity is shown in the following table.

$$\begin{array}{c|c|c|c|c|c|} \hline \text { Time since brakes applied (seconds) } & {0} & {3} & {6} & {9} & {12} \\ \hline \text { velocity (ft/sec) } & {80} & {62} & {47} & {32} & {22} \\ \hline \end{array}$$

Use a left sum to approximate the total distance the car has traveled over the 12 second interval.

Find the center and the radius of the given circle. $x^{2}+y^{2}=25$

Complete each statement. A tangent is ___ to the radius drawn to the point of tangency.

Find the radius of curvature of y=ln(x+1) at point (2, ln3).

Graph the equation. Give the radius of the circle.

$$x^2+y^2=10$$

A spherical balloon is inflated with helium at the rate of 100π ft³/min. How fast is the balloon's radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing?

A singly ionized helium ion has only one electron and is denoted $\mathrm{He}^{+}.$ What is the ion’s radius in the ground state compared to the Bohr radius of hydrogen atom?

Find the indicated measure. Area of a circle with a radius of 6.1 yards