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Several Questions on Rational Expressions

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There are several questions on rational expressions. Some have been shown here. Please take a look at the wk_4_cp_template.doc for the rest questions.

1) If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?

2) A passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, find the speed of each.

3) Ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

4) A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

5) Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?

6) Fungicides account for 1/10 of the pesticides used in the
United States. Insecticides account for ¼ of all the pesticides used in the United States. The ratio of fungicides to insecticides used in the United States can be written 1/10 ÷ ¼. Write this ratio in simplest form.

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10 Theory Questions and 4 Problems (with many parts) - See the attached question file for all the questions.

Theory Questions:

1. Post a response to the following: How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division?
2. Post a 50-word response to the following: How do you determine if a polynomial is the difference of two squares?
3. Post a response to the following: Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it first and then solve it. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.
4. Post a response to the following: How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life?
5. Post a 50-word response to the following: When solving a rational equation, why is it necessary to perform a check?
6. Post a response to the following: Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for the assignment to simplify.
7. Post a 50-word response to the following: What is the Pythagorean Theorem? How is it used?
8. Post a response to the following: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. Provide your answer with one or two solutions with which they must create a quadratic equation.
9. Post a response to the following: Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Why?
10. Post a 50 word response to the following: If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are?

Problems:

1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).
2. The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values.
3. In 2002, Home Depot's sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000.
4. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall (see figure). How long should the pieces of PVC plumbing pipe be?
The cost, in millions of dollars, to remove x % of pollution in a lake modeled by
1. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test.
2. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of the earth.
2. The equation gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).

[See the Attached Questions File for all the questions.]

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