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- You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…Solve: yv + 10yiv + 53y''' + 124y'' + 100y' = 0 a. y = C1e3xcos4x + C2e3xsin4x + C3e-2x + C4xe-2x + C5 b. y = C1e-3xcos4x + C2e-3xsin4x + C3e-2x + C4xe-2x + C5 c. y = C1e-3xcos4x + C2e-3xsin4x + C3e2x + C4xe2x + C5 d. y = C1e3xcos4x + C2e3xsin4x + C3e2x + C4xe2x + C5
- (1,6) and perpendicular to 2x+7y=1An air traffic controller is monitoring two small planes flying at the same altitude. One isflying towards the control tower from the West at 120 miles per hour and is currently 5 milesaway from the tower. The other plane is now on top of the tower and flying South at 150miles per hour. In order to respect local safety rules the planes have to be always more than4 miles from each other, or fly at different altitudes. Should the controller order one of theplanes to change altitude, or will they always be farther than 4 miles from each other?A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/hr and run 8 km/hr, where should he land to reach B as soon as possible? (Assume that the speed of the water is negligible compared with the speed at which the man rows)
- Farmer S. Unkist has a fruit grove consisting of lemons, bananas, and watermelons along a straight moat. To prevent thieves from stealing his fruit while at the same time make sure the fruit do not mix before they are processed, he plans to fence in each fruit plot using identical rectangular enclosures. The side along the moat needs no fence because the moat is infested with man eating crocodiles as shown below. If he has 1200 yards of fence, what should be the dimensions of each enclosure if the total area of the grove is to be maximized? PLEASE USE CALCULUS TECHNIQUES TO OBTAIN YOUR ANSWER AND SHOW ALL WORK.Lane 1 at your local track is 0.24 mi long. You live 0.5 mi away from the track. Which of the following results in the shortest term? a). Jogging 6 times around the track in Lane 1. b). Jogging to the track and then 5 times around the track in Lane 1. c). Jogging to the track, 3 times around the track in Lane 1, and then home. d). Jogging 8 times around the track in Lane 1.Solve for x , y, z, and w by Gauss Elimination Method Method
- . A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h and run 8 km/h, where should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared with the speed at whichthe man rows.)Want solution of part#aA small island is 3 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 15 miles down the shore from P in the least time?
