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The mean distance of Earth from the Sun is \(9.29 \times 10^{7}\) miles. Assuming that the orbit of Earth around the Sun is circular and that 1 revolution takes 365 days, find the linear speed of Earth. Express your answer in miles per hour.

Find the exact value of \(\tan 40^{\circ}+\tan 140^{\circ} .\)

A spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested? Express your answer in miles per hour. At how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour?

At the Cable Car Museum you can see the four cable lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour, driven by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

Designing a Little League Field For a 60 -foot Little League Baseball field, the distance from home base to the nearest fence (or other obstruction) in fair territory should be a minimum of 200 feet. The commissioner of parks and recreation is making plans for a new 60 -foot field. Because of limited ground availability, he will use the minimum required distance to the outficld fence. To increase safety, however, he plans to include a 10 -foot wide warning track on the inside of the fence. To further increase safety, the fence and warning track will extend both directions into foul territory. In total, the arc formed by the outfield fence (including the extensions into the foul territories) will be subtended by a central angle at home plate measuring \(96^{\circ}\), as illustrated. (a) Determine the length of the outfield fence. (b) Determine the area of the warning track.

Challenge Problem Let the Dog Roam A dog is attached to a 9-foot rope fastened to the outside corner of a fenced-in garden that measures 6 feet by 10 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander. Write the exact area in square feet.

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve: \(4^{x+3}=\frac{2^{x}}{16}\)

Explain the difference between linear speed and angular speed.

For a circle of radius \(r\), a central angle of \(\theta\) degrees subtends an arc whose length \(s\) is \(s=\frac{\pi}{180} r \theta .\) Discuss whether this statement is true or false. Defend your position.