The Area of a rectangle is represented by​ x^4 - y^4 / 8xy ​and its length is represented by x^2 - y^2 / 2xyWhat is the width of the rectangle?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: (1 / x-4) - (3x / x^2 -16)Subtract the rational expressionsGiven the equation (1 / x-4) - (3x / x^2 -16) = 2 / x + 4 solve the equation using your solution from part a.Solve the equation (1 / x - 4) - (3x / x^2 -16) = 2 / x + 4 using LCD.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)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.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.Write a function that gives the annual cost of a new refrigerator as a function of the number of years you own the refrigerator.What are the asymptotes of the rational function in part d? What does the horizontal asymptote mean in the context of this problem?Sketch the graph of the rational function from part c.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.

Assignment: Introduction to Quantitative Analysis: Confidence Intervals In your Week 2 Assignment, you displayed data based on a categorical variable and continuous variable from a specific dataset. In Week 3, you used the same variables as in Week 2 to perform a descriptive analysis of the data. For this Assignment, you will calculate a confidence interval in SPSS for one of the variables from your Week 2 and Week 3 Assignments. To prepare for this Assignment: Review the Learning Resources related to probability, sampling distributions, and confidence intervals. For additional support, review the Skill Builder: Confidence Intervals and the Skill Builder: Sampling Distributions, which you can find by navigating back to your Blackboard Course Home Page. From there, locate the Skill Builder link in the left navigation pane. Using the SPSS software, open the Afrobarometer dataset or the High School Longitudinal Study dataset (whichever you chose) from Week 2. Choose an appropriate variable from Weeks 2 and 3 and calculate a confidence interval in SPSS. Once you perform your confidence interval, review Chapter 5 and 11 of the Wagner text to understand how to copy and paste your output into your Word document. For this Assignment: Write a 2- to 3-paragraph analysis of your results and include a copy and paste of the appropriate visual display of the data into your document. If you are using the Afrobarometer Dataset, report the mean of Q1 (Age). If you are using the HS Long Survey Dataset, report the mean of X1SES. Based on the results of your data in this confidence interval Assignment, provide a brief explanation of what the implications for social change might be.