MATH 840 Homework 5 Due 2012-02-21

Instructions: To get full credit you must: (1) attempt and (2) traffic light all problems. If youget stuck in a problem and can’t proceed, explain where you are stuck. Be sure to answer thehomework on 81

2 x 11 white paper, using only one side of the paper. Please paperclip your pagestogether.

1. Choose a mathematics topic that you want to learn more about, and read about it online orin the textbook. Write a short explanation to teach what you learned, as if you were teachinga classmate who didn’t already understand the topic (if you didn’t learn anything, you didn’tread enough!).

2. Choose one of the problems you solved on either a previous homework, exam, or in-classassignment. Write your original solution. Then analyze the solution in terms of execution,explanation, and justification. Write down at least two ways in which you could improve theoriginal solution.

3. Based on your answer to the previous question, rework the problem that you just analyzedyour solution for (don’t just copy from the solutions!).

4. A classmate solved the following problem on the exam: A car rental agency charges $180 perweek plus $0.25 per mile to rent a car. How many miles can you travel in one week if youhave $395? A copy of your classmate’s work is given:

a. How could your classmate improve his or her explanation? Write a sentence that you couldadd to their solution to make it more clear.

b. How could your classmate improve his or her justification? Write a sentence that you couldadd to their solution to improve it.

5. (problem) Peter is a cross-country runner. He began a run at 2 p.m. This line graph showshis running times.

a. What is the total distance of his run?

b. How long does he take to complete his run?

c. How far does he run in the first five minutes?

d. What happened from about 2:15 until about 2:20?

e. Between which times did he run the fastest?

f. How far did he run between 2:25 and 2:40?

g. What was his average speed per minute? Explain how you figured this out.

6. (problem) The graphs below represent different aspects of driving.

a. The distance traveled during a journey at a steady speed.

b. The amount of gas left in the tank at different stages of a journey when traveling at asteady speed.

c. The price different people pay when they buy different amounts of gas from the samepump.

d. The time taken to make a journey at different speeds.

One of these graphs represents two of the above situations.

For each situation, say which graph it is represented by, and explain your reasoning.

7. (problem) Draw a graph to represent the following situation. Be sure to label your graph,and explain why you drew what you did. It takes you 30 minutes to travel 5 miles by bus.After getting off of the bus you walk for 15 minutes, to travel another mile. Then, you spend50 minutes in math class. Afterward you walk back to the bus stop and ride the bus home.

8. (problem) In San Francisco, the sales tax is 8.75%. If we let T represent the cost of an itemafter taxes, and C the cost before taxes, we find that

T (C) = 1.0875 · C.

a. If an item costs $200 before tax is charged, how much does it cost after taxes?

b. If an item costs $135 after taxes, write an equation for the cost of an item before taxes.Explain what the parts of your equation mean.

c. Explain in words what T ($25) means.

9. (exercises) Solve for x.

a. 4x− 12x + 23 = 3

4 + x

b. x + y + z = 2x + 2y

c. x3 + 1

6 = 212

d. 3x = x

e. 2x = 1

10. (problem) A model of an individual’s maximum heart rate is given by the function

H(a) = 220 − a,

where a is the individual’s age in years. Draw a graph that shows target heart rate for 5different ages. Be sure to label your graph, and choose appropriate ranges for the input andoutput variables. Explain why you chose the points that you did.

11. (problem) Google’s advertising revenue for the years 2006-2011 is given in the table below.Draw a graph to represent these data, and explain what it tells you.

Advertising Revenue (billions of USD) Year

36.531 201128.236 201022.889 200921.128 200816.142 200710.492 2006

12. (problem) The area of a square A as a function of its side length x is given by

A(x) = x · x.

Plot 5 points on a graph to show illustrate this relationship. Be sure to choose an appropriaterange, label your graph, and explain why you chose the values that you did.

13. (problem) A sofa normally sells for $840, but is on sale for $714. Find the percent decreasein the sofa’s price.

14. (problem) An American football field is a rectangle with a perimeter of 1040 feet. The lengthis 200 feet more than the width. Find the width and length of the rectangular field.