Create an equation and sketch the graph of a function using the following table: Time 0 15 30 45 60 75 90 105 120 Height 3.83 5 3.83 1 -1.83 -3 -1.83 1 3.83
Q: Let x, y, and z be real numbers. Prove the following a. -(-x) = x b. (-x) * (y) = -(xy) and (-x) *…
A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…
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Q: Consider the following LPP: maximize subject to ax1 + 1x2 -x₁ + x₂ <2 1 2 x1 + x₂ ≤ 3 1+2 X1, X2 ≥ 0
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A: As asked we shall solve only part d.
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A: We will find the value of the given integral.
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A: Since you have posted a question with multiple subparts, we will solve the first three subparts…
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Q: Find the general solution of the given higher-order differential equation. y''' - 2y'' - 3y' = 0
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Q: I don't understand this.
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Q: Solve the given differential equation by undetermined coefficients. y'' - 12y' + 36y = 24x + 5
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- Determine whether the graph below represents a one-to-one function.Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.Draw a sketch of the square and cube functions. What are the similarities and differences in the graphs?
- Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it appears to beexponential find a function that passes through the points.The average annual major league baseball player's salary for each year since free agency is approximated by the function S(x) = 74,741(1.17)* where x = 0 corresponds to 1976, and so on, up to x= 18 representing 1994. The salary is in dollars. What was the approximate average salary in 1988? $4 (Simplify your answer. Type an integer. Round to the nearest dollar if needed.)If $2400 is invested for x years at 13% interest, compounded annually, the future value that results is S= 2400(1.13) dollars. a. Graph the function for x = 0 to x= 8. b. Use the graph to estimate when the money in the account will double. a. Choose the correct graph below. OA. OB. OC. O D. -2400 -3600- -4800- -6000- -2400 6000- 4800- 360어 2400- 6000- 4800- -3600- -4800- 3600- -6000- 2400- 0 2 4 6 8 b. Choose the correct estimated answer about when the money in the account will double O A. after 6 years O B. after 2 years O C. after 4 years O D. after 7 years
- The graph of the function shown to the right illustrates a certain stock market index for the year 2010. Each tic mark on the horizontal axis represents the first opeing day of the market for that given month. Use the graph to answer parts (a) through (h). a. Over which month(s) did the index decrease? select all that apply. Jan, Feb, Mar, Apr, May, June, July, Aug, Sep, Oct, Nov, Dec. b. Over which month(s) did the index stay relatively the same? Select all that apply. Jan, Feb, Mar, Apr, May, June, July, Aug, Sep, Oct, Nov, Dec. c. Over which month(s) did the index increase? Select all that apply Jan, Feb, Mar, Apr, May, June, July, Aug, Sep, Oct, Nov, Dec. d. Over the month of _______ The value increased most rapidly. e. Approximate the index's value at the beginning of 2010. The index's value was approximately $____. f. Approximate its value at the end of 2010. The index's value was approximately $____. g. Approximately how much did the index's value increase over 2010.…The following graph approximates the number of pharmacists in a country in the years from 2002 through 2012. The number of pharmacists is a function g of the year x. Approximate the number of pharmacists in 2006. The number of pharmacists in a country in 2006 was approximately _____ thousands.A car was purchased for $22,500. Asume that is depreciates in value by 6% per year. Find a function V that models the value of the car after t years. Use the function to estimate the value after 8 years and 12 years.
- The graph of the function shown to the right illustrates a certain stock market index for the year 2010. Each tic mark on the horizontal axis represents the first opening day of the market for that given month. Use the graph to answer the following parts. a. Over which month(s) did the index decrease? Select all that apply. Jan, Feb, Mar, Apr, May, June, July, August, Sep, Oct, Nov, Dec b. b. Over which month(s) did the index stay relatively the same? Select all that apply. Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec c. Over which month(s) did the index increase? Select all that apply. Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec d. over the month of _____the value was increased most rapidly. *Please be accurateA user is charged P500.00 monthly for a particular mobile plan, which includes P150.00 free text messages. Messages in excess of 150 are charged P1.00 each. Represent the amount a consumer pays each month as a function of the number of messages m sent in a month.