This project uses the content and information covered in Units 4 and 5.

In the real work world, you will be assigned tasks to complete with deadlines. Your job depends on meeting those deadlines and providing accurate and reliable information. Do not procrastinate!

Your submittal for this project should look like a work product that you would submit to a boss or supervisor. That means that you should provide narrative that explains what you are doing and, yes, spelling and formatting count. Use appropriate and precise mathematical notation. Use an Equation Editor for clarity. Your ultimate goal is to prove you understand and can use the concepts of Units 4 and 5.

You may want to run your finished project by someone who may not even understand the math to see if they can follow your layout and narrative. That would be a good test of the quality of your work.

PART ONE: 100 points

a) (20 pts.) You work for a security systems company and need to install a security camera in a jewelry store. The camera will be mounted on a wall 9 feet above the floor. If the camera is directed to the cash register, a spot 12 feet from the wall and 6 feet above the floor, what is the angle of depression?

b) (20 pts.) There are two ranger towers in a wilderness area. Tower #1 is 150 miles due south of Tower #2. You are lost in the wilderness area and your emergency beacon sends out a call that reaches both towers. Tower #1 indicates that you are located at N55^{o}E. Tower #2 indicates that you are located at S60^{o}E. How far is each tower from you? If a helicopter that flies at 200 miles per hour leaves the nearest tower, how long, in minutes, will it take to reach you?

c) (20 pts.) You are a great parent and are going to build a swing set for your children. It will have an A frame structure. You will construct the support ends with two 10-foot long 4” by 4” boards joined at a 45^{o} angle. Thinking of safety, you realize the swing set may tip over. So you decide to anchor each leg in concrete footings. How far apart should the footings for each A frame be?

d) 20 pts. You are a surveyor and you need to determine the approximate area of an irregularly shaped sinkhole. You don’t want to get too close, it might open up more. So, you walk around the sinkhole and take measurements (see the figure below). What is the approximate area of the sinkhole? [**Hint**: Use the Law of Cosines on the three triangles shown and then find the sum of their areas.]

e) (20 pts.) As a student of electricity, you will learn that the voltage *V* (in volts) across a capacitor will gradually diminish to 0 with time *t* (in seconds). The function relating *V* to *t *is:. What times t does the graph of V touch the graph of When does the graph of V touch the graph of When will the voltage *V* be between -0.4 and 0.4 volts?

**PART TWO: 100 Points**

a) (10 pts.) Given the polar coordinates (-2, ), find the rectangular coordinates.

b) (10 pts.) Given the rectangular coordinates (8.3, 4.2), find the polar coordinates.

c) (10 pts.) Given 2x^{2} + 2y^{2} = 3, write the equation using polar coordinates (r, θ).

d) (10 pts.) Given r^{2} = cos θ, write the equation using rectangular coordinates (x, y).

e) (20 pts.) A passenger jet maintains a speed of 550 miles per hour headed due north. The Jet Stream is 100 miles per hour in a northeasterly direction. As the navigator, express the velocity **v**_{a} of the jet relative to the air and the velocity **v**_{w} of the jet stream in terms of **i** and **j**. Find the velocity of the jet relative to the ground. Find the actual speed and direction of the jet relative to the ground.

f) (20 pts.) You are a home owner who is interested in solar energy for your home. You learn that the amount of energy collected by a panel depends on the intensity of the sun’s rays and the area of the panel. The vector** I** represents the intensity in watts per square centimeters. The vector **A** represents the area in square centimeters whose direction is the solar panel orientation. The total number of watts collected by the panel is given by W = |** I** ● **A** |. Suppose that **I** = and **A** = . Find || **I** || and || **A **||. Compute W. If the solar panel is to collect the maximum number of watts, what must be true about **I **and **A**?

g) (20 pts.) You parked a moving van that has a gross weight of 8000 pounds on a street with a 5% grade. Find the magnitude of the force required to keep the van from rolling down the hill. What is the magnitude of the force perpendicular to the hill?

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