the area of a rectangle is represented by fraction numerator x to the power of 4 minus y to the power of 4 over denominator 8 x y end fraction and its length is represented by fraction numerator x squared minus y squared over denominator 2 x y end fract

1. The Area of a rectangle is represented by fraction numerator x to the power of 4 minus y to the power of 4 over denominator 8 x y end fraction and its length is represented by fraction numerator x squared minus y squared over denominator 2 x y end fraction.

  1. What is the width of the rectangle?
  2. If you double the length of the rectangle but keep the same width, what is the new area of the rectangle?

2. Consider the following expression:

fraction numerator 1 over denominator x minus 4 end fraction minus fraction numerator 3 x over denominator x squared minus 16 end fraction

  1. Subtract the rational expressions
  2. Given the equation fraction numerator 1 over denominator x minus 4 end fraction minus fraction numerator 3 x over denominator x squared minus 16 space end fraction equals fraction numerator 2 over denominator x plus 4 end fraction, solve the equation using your solution from part a.
  3. Solve the equation fraction numerator 1 over denominator x minus 4 end fraction minus space fraction numerator 3 x over denominator x squared minus 16 end fraction equals fraction numerator 2 over denominator x plus 4 end fraction using LCD.
  4. Compare the methods used to solve the equation in parts c and d. Which method do you think is better and why?

3. The average cost of electricity used for an 18 cubic ft. refrigerator that is 10 years old is $128 per year. A new refrigerator the same size costs about $81 per year for electricity. (Source: https://www.efficiencyvermont.com)

  1. Suppose a new refrigerator costs $500. Determine the total cost of having either refrigerator for 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.
  2. Determine the total annual cost for a new refrigerator that lasts 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.
  3. Write a function that gives the annual cost of a new refrigerator as a function of the number of years you own the refrigerator.
  4. What are the asymptotes of the rational function in part d? What does the horizontal asymptote mean in the context of this problem?
  5. Sketch the graph of the rational function from part c.
  6. If you plan on owning your refrigerator for 12 years, would it be more cost effective to keep your old refrigerator or purchase a new one? Explain.

 

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