46) A famous comedian will appear at a comedy club for one performance. The equation R(p) 5p2 300p describes the relationship between the price of a ticket, p, in dollars, and the revenue, R, in dollars, from ticket sales. That is, the revenue is a function of price. a) Determine the club’s revenue from ticket sales if the price of a ticket is $40. b) Determine the club’s revenue from ticket sales if the price of a ticket is $25. c) If the club is expecting its revenue from ticket sales to be $4500, how much should it charge for each ticket? 47) An object is launched upward from the ground with an initial velocity of 200 ft/sec. The height h (in feet) of the object after t sec is given by h(t) 16t2 200t. a) Find the height of the object after 1 sec. b) Find the height of the object after 4 sec. c) When is the object 400 ft above the ground? d) How long does it take for the object to hit the ground? 48) The equation R(p) 7p2 700p describes the revenue from ticket sales, R, in dollars, as a function of the price, p, in dollars, of a ticket to a fundraising dinner. That is, the revenue is a function of price. a) Determine the revenue if the ticket price is $40. b) Determine the revenue if the group sells each ticket for $70. c) If the goal of the organizers is to have ticket revenue of $17,500, how much should it charge for each ticket? a) How high is the shell after 3 sec? b) Find the shell’s horizontal distance from the mortar after 3 sec. c) The shell explodes after 8.25 sec. What is its height when it bursts? d) What is the shell’s horizontal distance from its launching point when it explodes? (Round to the nearest foot.) e) Compare your answers to 43a) and 44a). What is the difference in their heights after 3 sec? f ) Compare your answers to 43c) and 44c). What is the difference in the shells’ heights when they burst? g) Assuming that the technicians timed the fi rings of the 3-in. shell and the 10-in. shell so that they exploded at the same time, how far apart would their respective mortars need to be so that the 10-in. shell would burst directly above the 3-in. shell? 45) The senior class at Richmont High School is selling t-shirts to raise money for its prom. The equation R(p) 25p2 600p describes the revenue, R, in dollars, as a function of the price, p, in dollars, of a t-shirt. That is, the revenue is a function of price. a) Determine the revenue if the group sells each shirt for $10. b) Determine the revenue if the group sells each shirt for $15. c) If the senior class hopes to have a revenue of $3600, how much should it charge for each t-shirt? R1) What is an application problem? R2) Do you think a calculator can solve quadratic equations for you? How will a calculator help you solve the problems in this application section? R3) Why do you sometimes eliminate negative solutions when you are solving application problems involving quadratic equations? R4) What types of college courses do you think often use quadratic equations to solve application problems? R5) Which exercises in this section do you fi nd most challenging? Group Activity – The Group Activity can be found online on Connect. 412 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
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