91Ó°ÊÓ

Adam must fly home to St. Louis from a business meeting in Oklahoma City. One flight option flies directly to St. Louis, a distance of about 461.1 miles. A second flight option flies first to Kansas City and then connects to St. Louis. The bearing from Oklahoma City to Kansas City is N29.6 \({ }^{\circ} \mathrm{E}\), and the bearing from Oklahoma City to St. Louis is N57.7 \(^{\circ}\) E. The bearing from St. Louis to Oklahoma City is \(S 57.7^{\circ}\) W, and the bearing from St. Louis to Kansas City is \(\mathrm{N} 79.4^{\circ} \mathrm{W}\). How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight?

The Bermuda Triangle is roughly defined by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. The distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton are approximately \(1028,1046,\) and 965 miles, respectively. Ignoring the curvature of Earth, approximate the area of the Bermuda Triangle.

Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates the bearing of the ship is \(\mathrm{N} 55^{\circ} \mathrm{E} ;\) the call to Station Baker indicates the bearing of the ship is \(\mathrm{S} 60^{\circ} \mathrm{E}\). (a) How far is each station from the ship? (b) If a helicopter capable of flying 200 miles per hour is dispatched from the station nearest the ship, how long will it take to reach the ship?

A major league baseball diamond is actually a square 90 feet on a side. The pitching rubber is located 60.5 feet from home plate on a line joining home plate and second base. (a) How far is it from the pitching rubber to first base? (b) How far is it from the pitching rubber to second base? (c) If a pitcher faces home plate, through what angle does he need to turn to face first base?

There is a Heron-type formula that can be used to find the area of a general quadrilateral. $$K=\sqrt{(s-a)(s-b)(s-c)(s-d)-a b c d \cos ^{2} \theta}$$ where \(a, b, c,\) and \(d\) are the side lengths, \(\theta\) is half the sum of two opposite angles, and \(s\) is half the perimeter. Show that if a triangle is considered a quadrilateral with one side equal to \(0,\) Bretschneider's Formula reduces to Heron's Formula.

According to Little League baseball official regulations, the diamond is a square 60 feet on a side. The pitching rubber is located 46 feet from home plate on a line joining home plate and second base (a) How far is it from the pitching rubber to first base? (b) How far is it from the pitching rubber to second base? (c) If a pitcher faces home plate, through what angle does he need to turn to face first base?

A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rope 100 feet long. What is the maximum grazing area for the cow?

Colossus Added to Six Flags St. Louis in \(1986,\) the Colossus is a giant Ferris wheel. Its diameter is 165 feet; it rotates at a rate of about 1.6 revolutions per minute; and the bottom of the wheel is 15 feet above the ground. Find a function that relates a rider's height \(h\) above the ground at time \(t\). Assume the passenger begins the ride at the bottom of the wheel.

A perfect triangle is one having integers for sides for which the area is numerically equal to the perimeter. Show that the triangles with the given side lengths are perfect. (a) 9,10,17 (b) 6,25,29

Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the function \(d(t)=a \sin (\omega t)\) If a tuning fork for the note A above middle \(\mathrm{C}\) on an even-tempered scale \(\left(A_{4},\right.\) the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find \(\omega\). If the maximum displacement of the end of the tuning fork is 0.01 millimeter, find a function that describes the movement of the tuning fork.