82 please XRevathi Narasimhan, College Alge X X Revathi Narasimhan, College Alge X← → C ✰ xyztextbooks.com/ebook/title/reva_caE CONTENTS24073°FClearCATALOGChapter 3 Polynomial and Rational Functions+SECTION: 3.1Applications80. Landscaping A rectangular garden plot is to be enclosed, with a fence on three of its sides anda brick wall on the fourth side. If 100 feet of fencing material is available, what dimensions willyield the maximum area?+ xPAGE 24081. Construction A rectangular fence is being constructed around a new play area at a localelementary school. If the school has 2000 feet of fencing available for the project, what is themaximum area that can be enclosed for the new play area?82. Physics: Ball Height A cannonball is fired at an angle of inclination of 45° to the horizontal witha velocity of 50 feet per second. The height h of the cannonball is given by-32x²h(x) =(50)²where x is the horizontal distance of the cannonball from the end of the cannon.a. How far away from the cannon should a person stand if the person wants to be directly belowthe cannonball when its height is maxiumum?b. What is the maximum height of the cannonball?83. Physics: Ball Height The height of a ball that is thrown directly upward from a point 200 feet abovethe ground with an initial velocity of 40 feet per second is given by h(t) = -16t² + 40t + 200,where t is the amount of time elapsed since the ball was thrown. Here, t is in seconds and h(t)is in feet.a. Sketch a graph of h.b. When will the ball reach its maximum height, and what is the maximum height?84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up aflat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open.aCCVIDEOSMr. Hampton▶ PlayBOOKSHELFSUPPLEMENTSm(x) = -0.0108X² +0.981 X + 8.0530-b) mileage 35mphm(35) =-0.0108(35)² +15-0.98 (39)+8.05 19.29.2 mpg20.CCmaximum, using a graphing utility.Shelby▶ Play5hat speed is mileage at a maximumV=(45.5, 30.4)PROGRESS0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75CCBreylor▶ PlayESm(x)-0:00Math1xTOOLS IIIссCCJulieta▶ Play[]españolX8:08 PM10/20/202220

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-32x² (50)² h(x) where x is the horizontal distance of the cannonball from the end of the cannon. a. How far away from the cannon should a person stand if the person wants to be directly below the cannonball when its height is maxiumum? +x