61 please Um in the60. Doppler Effect The Doppler effect (named after ChristianDoppler) is the change in the pitch (frequency) of thesound from a source (s) as heard by an observer (0) whenone or both are in motion, If we assume both the sourceand the observer are moving in the same direction, therelationship istext with the new layout at the beginning of the studyvolume of 100 cubic feet.drum as a function of the radius r of the cylinder.shape of a right ĉircular cyinder is required to have(a) Express the amount A of material required to make the(b) How much material is required if the drum's radius i(c) How much material is required if the drum's radvus i(d) How much material is required if the drum's radius i(e) Graph A = A(r). For what value of r is A(a) What was the average number of words users couldwhere t is the number of days of practice with the keyboard(b) What was the average number of words users coul(c) Find and interpret the horizontal asymptote of N.f' =where f = perceived pitch by the observerf. = actual pitch of the sourcev = speed of sound in air (assume 772.4 mph)V, = speed of the observerV, = speed of the source3 feet?Suppose that you are traveling down a road at 45 mph andyou hear an ambulance (with siren) coming toward youfrom the rear. The actual pitch of the siren is 600 hertz (Hz).(a) Write a function f" (v,) that describes this scenario.(b) If f' = 620 Hz, find the speed of the ambulance.E (c) Use a graphing utility to graph the function.(d) Verify your answer from part (b).Source: www.acs.psu.edu/drussel/4 feet?5 feet?smallest?65. Tennis Anyone? To win a game in tennis, a player musfour points. If both players have won three points, the nlucontinues until a player is ahead by two points to win thegame. The model61. Minimizing Surface Area United Parcel Service hasA contracted you to design a closed box with a square basethat has a volume of 10,000 cubic inches. See the illustration.(a) Express the surface area S of the box asa function of x.x*(-8x + 28x² – 34x + 15)2x2 – 2x + 1P(x) =(b) Using a graphing utility, graph thefunction found in part (a).(c) What is the minimum amount ofcardboard that can be used to constructthe box?represents the probability P of a player winning a game inwhich the player is serving the game and x is the probabiliyof winning a point on serve. The player serving is the firstoput the ball in play.Source: Chris Gray, “Game, set and stats," SignificanczFebruary 2015.(d) What are the dimensions of the box that minimize thesurface area?(e) Why might UPS be interested in designing a box thatminimizes the surface area?(a) What is the probability that a player who is serving wilwin the game if the probability of the player winning apoint on serve is 0.64?(b) Find and interpret P(0.62).(c) Solve P(x) = 0.9.(d) Graph P = P(x) for 0 s xs 1. Describe whlhappens to P as x approaches 1.66. Texting Speed A study of a new keyboard layour lesmartphones found that the average number of wordsecould text per minute could be approximated by62. Minimizing Surface Area United ParcelService has contracted you to design an openbox with a square base that has a volumeof 5000 cubic inches. See the illustration.y(a) Express the surface area S of the box asa function of x,(b) Using a graphing utility, graph the function foundin part (a).(c) What is the minimum amount of cardboard that can beused(d) What are the dimensions of the box that minjmize theconstruct the box?32 (t + 2)surface area?(e) Why might UPS be interested in designing a box thatN(t)%3Dt + 5minimizes the surface area?63. Cost of a Can A can in the shape of a right circular cylinderis required to have a volume of 500 cubic centimeters. Thetop and bottom are made of material that costs 6g persquare centimeter, while the sides are made of material thatcosts 4ç per square centimeter.text after using the layout for 1 week?(a) Express the total cost C of the material as a function ofthe radius r of the cylinder. (Refer to Figure 43.)(b) Graph C = C(r). For what value of r is the cost Caminimum?'Ar

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61. Minimizing Surface Area United Parcel Service h. contracted you to design a closed box with a square bas that has a volume of 10,000 cubic inches, See the illustratio. (a) Express the surface area S of the box as a function of x. (b) Using a graphing utility, graph the function found in part (a). (c) What is the minimum amount of cardboard the X.