A basketball player attempts a foul shot from the foul line. The path of the basketball is given by the function H(x)＝−0.068x 2 +1.17x+7, where His measured in feet above the ground and xis the horizontal distance from the foul line in feet. 1.) How high above the ground was the basketball when the player released the basketball? (Don′t forget to include units) 2.) What was the basketball′s maximum height above the ground, and what was the horizontal distance between the basketball and the player when the ball reached the maximum height? (Round answers to two decimal places if needed). The Tucson Sun Link administration team estimates that for each $0.25 increase in the price of a ticket, the number of monthly riders decreases by 2000 people. The current price of a ticket is $4; at this price, there are currently 60,000 monthly riders. 1.) What is the monthly revenue given the current price for a ticket? (Make sure to include units) 2.) (part b) Write an equation that represents the monthly revenue as a function of the price of a ticket. (Make sure to define your variables) 3.) Use your equation from Part b) to determine the price Sun Link should charge in order to maximize monthly revenue and to determine the maximum monthly revenue. A student launches a toy model rocket from the top of a building. The rocket lands on a target on the ground below (shattering to pieces after the parachute fails to open). The equation for the rocket′s height in meters is given by A(t)＝− 10 4 (x−30) 2 +600where tis the time in seconds after launch. Use the equation (not a graph) to answer the following questions. 1.) How high is the building that the rocket was launched from? (Make sure to include units) 2.) What was the greatest height that the rocket reached, and how long after launch did it reach this height? (Make sure to include units) 3.) When did the rocket land? (Round your answer to two decimal places, and make sure to include units) The opening value of a stock index on the first day of trading from 1994 to 2010 can be modeled using the following polynomial: N(t)＝11.8690t 3 +20.3119t 2 +22.0273t+757.2156where tis time in years since 1994. 1.) What is the y-intercept and what does this tell you in practical terms? 2.) What does this model tell you is the opening value of the stock index on the first day of trading in 2004? (15,108 is the actual number for that year). 3.) Graph this function in an appropriate window, label completely. A company designs fish tanks of various sizes. Because of shipping restrictions, a fish tank′s height (1 vertical edge) and the entire perimeter of the base (4 edges along the bottom) cannot be more than 270 centimeters altogether (the total of all 5 edges). 1.). (Part A) Suppose the company wants to ship a fish tank that has a SQUARE BASE (the dimensions of the bottom of the fish tank are equal, similar to the image in attachment). If the fish tank has a length of 15 centimeters along one edge of the bottom, how tall can the fish tank be? (Don′t forget to include units) 2.) What is the volume of the fish tank from Part a)? 3.) Write a function to represent the volume of a fish tank with a SQUARE BASE of length xfor one edge, still using the total sum of the height and perimeter of the base equal to 270 centimeters altogether.
