These exercises involve the formula for the length of a circular arc. A circular arc of length 25 ft subtends a central angle of

$$50 ^ { \circ }$$

. Find the radius of the circle.

A sector of a circle of radius $24 \text{mi}$ has an area of $288 \text{mi}^2$. Find the central angle of the sector.

Find the sum of each arithmetic series.

$$\sum _ { n = 1 } ^ { 24 } ( 2 n - 1 )$$

Due to a decrease in the cost of materials, the profit function for Acme Innovations has changed to $Q(x)=-x^{3}+10 x^{2}+13 x-22 .$ How many lamps should they make in order to make a profit?

Match the correct graph $A–F$ to the function without using your calculator. Then, if you have a graphing calculator, use it to check your answers. Each graph in this group shows $x$ and $y$ in $[-10,10]$.

$$y=f(-x)$$

The standard equation of a circle with center at (2, -3) and radius 1 is _____.

The are of a square is 36 square inches. What is the length of each side?

If you know two angles of a triangle, then you can determine the third angle because the sum of all three angles is ______ degrees.

The current I flowing in a transistor radio t seconds after it is switched off is given by $I=I_{0} \times 2^{-0.02 t}$ amps. Show that it takes $\frac{50}{\log 2}$ seconds for the current to drop to 10% of its original value.

Two plane mirrors stand facing each other, 3.00 m apart, and a woman stands between them. The woman faces one of the mirrors from a distance of 1.00 m and holds her left arm out to the side of her body with the palm of her left hand facing the closer mirror. Does it show the palm of her hand or the back of her hand?

Find the directions of maximum and minimum change of f at the given point, and the values of the maximum and minimum rates of change. $f(x, y)=x^{2} \cos (3 x y)$, (2, 0)

Calculate. $\int\dfrac{\sinh x}{1+\cosh x}dx$

Graph a function $f(x)$ which is increasing everywhere and concave up for negative $x$ and concave down for positive $x$.

How do you determine your net pay?