FORMAT FOR "WRITTEN UP" HOMEWORK

Math 117

Periodically you will be asked to writeup some homework problems. Explaining your work is just as important as the answer in these problems. You should use the procedure below for most problems that you attempt in class. However, when you writeup a problem you will be documenting the process that you use in solving a problem, explicitly describing each step. The outline below is a model. You may use other formats. The important thing is that you use English to communicate your thought processes and the mathematics that you use in solving a problem.

1) DEFINE THE SITUATION. Draw a diagram. What is given? Use variables to represent the given information. Label them in your diagram. Sketch a graph. Label coordinates, axes.

2) STATE THE OBJECTIVE. What does the question ask? What will the answer look like? Are units involved?

3) GENERATE IDEAS. Have you seen the problem before? Do you know a related problem? What formulas or theorems might be helpful? What concepts are involved in the problem?

4) PREPARE YOUR PLAN. Choose your method. Gather pertinent information and formulas.

5) TAKE ACTION. Execute your plan.

6) REVIEW. State your answer in its appropriate context. Is it reasonable? Can you check your result? Does your analytic solution agree with your geometric pictures? Are you using the appropriate units? Did you answer the question?

All six steps may not be appropriate for each problem. Do not write down steps for the purpose of writing steps. These papers should be neat and legible. These papers will be marked either 7, 8, 9, 10, or "redo". Papers that do not follow an appropriate format or have missed the point of the problem will be marked redo. These papers may be resubmitted up to 1 week after they are returned. If a "redo" is not resubmitted within the specified time period the grade will be a zero.

Example - #12, page 479, Demana and Waits

1. Define the situation. A boat travels at a speed of 40 mph from its home base on a course of 65 for two hours and then changes to a course of 155 for four hours.

2. State the objective. Determine the distance, d, from the boat to its home port and the bearing from the home port to the boat after the six hours.

3. Generate ideas. The course or bearing of the boat will be measured from due north moving clockwise. There is a right triangle in our diagram, the Pythagorean theorem (a2+b2 = c2) and right angle trig definitions will be appropriate.

4. Prepare the plan.

a) Consider the right triangle in our problem, determine the distance travelled on the two known sides based on speed and time travelled.

b) Solve for d.

c) Using trig when appropriate, determine angles in the diagram.

d) Determine the bearing of the present course.

5. Take action.

a)40 mph * 2 hours = 80 mi.

40 mph * 4 hours = 160 mi.

Since we have two sides of a right triangle we can determine the length of the other side with the Pythagorean theorem.

b) d2=802 + 1602

= 6400 + 25,600

= 32,000

d=

 + 178.89

Choose the positive root since d is a distance.

d= 178.89 mi.

c)Use trig functions to find á.

tan á= 2

á= tan-1(2)

= 63.43

d)The bearing, è, is measured from north, so that

è= á + 65

= 63.43 + 65

= 128.43

6. Review.

The boat is a distance of approximately 178.89 miles from its homeport. The bearing from its homeport is 128.43. This bearing agrees with the approximate direction in the sketch.