Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and the cities are on the same longitude (one city is due north of the other).

$$\begin{matrix} \text{City} & \text{Latitude}\\ \text{San Francisco, California} & \ {37^{\circ} 47^{\prime} 36^{\prime \prime} \mathrm{N}}\\ \text{Seattle, Washington} & \ {47^{\circ} 37^{\prime} 18^{\prime \prime} \mathrm{N}}\\ \end{matrix}$$

Find the radius r of a circle with an arc length s and a central angle $\theta$. Arc Length s: 82 miles Central Angle $\theta$: 135$^{\circ}$

Draw a diagram of this statement. Then answer the question. The first stage of the rocket fell from a height of 23,000 feet and settled on the ocean floor 9000 feet below sea level. In all, how many feet did the rocket's first stage descend?

A steel plate has the form of one-fourth of a circle with a radius of $60$ centimeters.Two two-centimeter holes are to be drilled in the plate positioned as shown in the figure. Find the coordinates of the center of each hole.

find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. r = 14 feet, s = 8 feet.

Write the augmented matrix for the system of linear equations.

$$\left\{\begin{aligned} 6 x-7 y &=11 \\-2 x+5 y &=-1 \end{aligned}\right.$$

A matrix and its characteristic polynomial are given. Find the eigenvalues of each matrix and determine a basis for each eigenspace.

$$\begin{equation*} \begin{bmatrix}-1&&4&&-4&&-4\\5&&-2&&1&&6\\0&&0&&-1&&0\\5&&-5&&5&&9\end{bmatrix}, -(t-3)(t-4)(t+1)^2.\end{equation*}$$

Find the number of roots for each equation. $x^{3}-2 x+5=0$

Use words to describe the rule of the following sequence. Then find the next two terms. 1, 10, 100, ...

The number of newly reported cases of HIV (in thousands) in the United States from 2000 to 2010 can be modeled by the following formula: $f(t)=41(0.9842)^{t}$ where t is the number of years after 2000. a. Identify the growth factor. b. Calculate the estimated number of new HIV cases reported in 2004. c. Graph the points $(t, f(t))$ for integer values of $0 \leq t \leq 10$. d. During what year did the number of newly reported HIV cases drop below 36,000?

Use the sequence $-32,16,-8,4, \dots$ What is the common ration?

What is the range of fuel efficiencies, in miles per gallon, you get with your car? At what speeds, in miles per hour, is the peak achieved?

Using appropriate software, investigate the effect of the condenser pressure on the COP of an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Assume the evaporator pressure is kept constant at 150 kPa while the condenser pressure is varied from 400 to 1400 kPa. Plot the COP of the refrigeration cycle against the condenser pressure, and discuss the results.

Find the area of each figure. If necessary, round to the nearest tenth. a square with side length 2 cm.