In Exercises 4-5, find the indicated function values. 4. f(x) = 7x – 5 а. f(0) b. f(3) c. f(-10) d. f(2a) 5. g(x) = 3x? – 5x + 2 е. f(а + 2) | b. g(5) a. g(0) d. g(b) c. g(-4) e. g(4a)
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- Two students were playing the same game. The difference in points that each scored for the game can be modeled by the function y=5sinx+3sinxcosx after x seconds. Within the interval 0<x<6, when does the function have a value of -1? Group of answer choices 3.146 seconds 3.592 seconds 5.682 seconds 5.128 secondsOne of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model. Table A x 0 1 2 3 4 f(x) 10 23 36 49 62 Table B x 0 1 2 3 4 g(x) 10 23 44 73 110 linear function ---Select--- f(x) g(x) = quadratic function ---Select--- f(x) g(x) =In Exercises 1–4, an object dropped from rest from the top of a tallbuilding falls y = 16t2 feet in the first t seconds. 1. Find the average speed during the first 3 seconds of fall.2. Find the average speed during the first 4 seconds of fall. 3. Find the speed of the object at t ! 3 seconds and confirm youranswer algebraically. 4. Find the speed of the object at t ! 4 seconds and confirm youranswer algebraically.
- for the function, find the relative maxima, relative minima, and horizontal points of inflection. Y=3x^5-5x^3+2 How are the steps to solve I am very confused.The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. P(x)=-.004x^2+10x-5000An analysis of passenger traffic at Daytona Beach International Airport over the past 40 years shows that the number of passengers using the airport each year can be modeled by the function P(x) = 134x3 - 8335x2 + 138,607x + 222,284, where x represents the number of years since 1980 and the domain is [0, 40]. Answer the following questions. All work must be shown. a. At what rate was the passenger traffic changing in 2015? Label and interpret your answer. b. Evaluate P(25), P ' (25), and P '' (25). Label and interpret the answers. What do these answers tell you about passenger traffic in that year? c. Determine the relative/absolute extrema of the function on the interval. Interpret the meaning of the answer. d. What is the POI and what does it tell you about passenger traffic?
- Student Loans Data for selected years from 2011and projected to 2023 can be used to show that thebalance of federal direct student loans y, in billions ofdollars, is related to the number of years after 2010,x, by the function y = 130.7x + 699.7.a. Graph the function for x-values corresponding2010 to 2025.b. Find the value of y when x is 13.c. What does this function predict the balance offederal direct student loans will be in 2029?(Source: U.S. Office of Management and Budget)The median size of a new single-family house built in the United States between 1987 and 2001 can be modeled by the equation H(x) = 0.359x3 − 15.198x2 + 221.738x + 862.514 square feet where x is the number of years after 1980. 1. Determine the value of x in the domain 7 ≤ x ≤ 21 for which the median house size was increasing least rapidly. (Round your answer to three decimal places.) 2. Thus, in which year was the median house size was increasing least rapidly? 3. Find the corresponding house size. (Round your answer to one decimal place.) 4. Find the corresponding rate of change in house size. (Round your answer to three decimal places.)Two students were playing the same game. The difference in points that each scored for the game can be modeled by the function y=5sinx+3sinxcosx. Within the interval 0<x<6, when is the difference in points the smallest? Group of answer choices 5.128 seconds 1.155 seconds 1.987 seconds 4.296 seconds
- Suppose that the selling price p of an item for the quantity x sold is given by the function p=-1/5 x +50 , 0<=x<=250 (c) What is the maximum revenue that can be obtained from this model?During the first quarter of the school year the officers –elect of the Supreme Student Government decided to divide their budget evenly to the different committees. If their budget is ₱35,000 construct a function M which would give the amount of money each of the n number of committees would receive.a. You may contruct a table to aid you in determining the relationships between quantities. Number of Committees 2 4 6 8Amount allocated foreach committeeb. Write the rational function that represents the situationScientists in Malaysia have collected data revealing that there is a linear relationship between the length (snout to vent) of the beaked sea snake and the length of its catfish prey such that l(x) = 2.41 + 0.12x, where x is the snout-vent length (cm) of the snake and l(x) is the predicted length (cm) of the catfish. Source: Biotropica. a. Use the function above to estimate the size of catfish that a snake which has a snout-vent length of 70 cm will choose for prey. b. Calculate the derivative of this function and interpret the results.