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- .20 D Show that fe conversion to polar coordinates. dx = √n by considering e-(x²+y²) dxdy and aarrow_forward6. Find the angle above the horizon of the airplane as seen by the observer. Problem 5. Two traffic cops are sitting stationary at positions ri = At t = 0, a car is at the origin with instantaneous velocity v. At that time, officers 1 and 2 measure line-of-sight speeds vi and v2 on their radar guns. Determine the car's velocity v at t = 0. î+j and r2 = -j, respectively.arrow_forwardQuèstion 12 The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. True O False A Moving to another question will save this response. ASUSarrow_forward
- As illustrated in the accompanying figure, suppose that a rod with one end fixed at the pole of a polar coordinate system rotates counterclockwise at the constant rate of 1 rad/s. At time t = 0 a bugon the rodis 10 mm from the pole and is moving outward along the rod at the constant speed of 2 mm/s.(a) Find an equation of the form r = f(θ)forthe path of motion of the bug,assuming that θ = 0when t = 0.(b) Find the distance the bug travels along the path in part (a) during the first 5 s.Round your answer to the nearest tenth of a millimeter.arrow_forward1. A space-ship is heading towards a planet, following the trajectory, r(t) = (Ae-¹² cos(3t), √2Ae-t² sin(3t), - Ae-t² cos(3t)), where A 50, 000km and the time is given in hours. (a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does the ship reach the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. (b) To 4 significant figures and including units, what are the velocity and speed of the space-ship when it reaches the planet?arrow_forwardThe motion of a particle is defined by the following equations: dx/dt = x-2y and dy/dt = 5x-y with x(0) = 2 and y(0) = -1 Find x(t) and y(t) If x(t) and y(t) are periodic, find their amplitudes and periods Which of the attached graphs represents the motion? (Circle answer) A B Neitherarrow_forward
- This problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 5 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y direction is down in this problem.) y = learrow_forwardQuestion 24arrow_forwardQUESTION 8 On some highways, a car can legally travel 20 km/hr faster than a truck. Travelling at maximum legal speeds, a car can travel 120 kms in 18 minutes less than a truck. What are the maximum legal speeds for cars and for trucks? Car = 110 km/hr & Truck = 90 km/hr Car = 120 km/hr & Truck = 100 km/hr Car = 100 km/hr & Truck = 80 km/hr %3D O Car = 90 km/hr & Truck = 70 km/hrarrow_forward
- Problem 3: Consider the functional: I = /1+yr2 dx . y a) Find the Euler-Lagrange equation, which minimizes that functional. b) Solve the Euler-Lagrange and show that the curve is a circle. c) Find the radius and the center of the circle.arrow_forwardpart d, e, farrow_forwardProblem 4 Lara plans to go on a short trip to the Netherlands on one of the next four weekends (T = 4). As she enjoys sunbathing and the weather will be getting better over time, we have v = (15,24, 33, 45). When on vacation, she is not able to take care of her tomato plants at home. The consequences of not watering the plants is more severe, the warmer it is. Accordingly, c = (3,6,9, 12). Going on vacation is an action with immediate rewards as it is enjoyable right now, but in late summer Lara might suffer from not being able to harvest tomatoes. Lara has a present bias of ß = and a long-run discount factor 6 = 1. (a) Derive Te, the period in which the TC (no present bias, B = 1) goes on vacation. Explain the behavior intuitively. (b) Derive T, the period in which the Naif goes on vacation. Explain the behavior intuitively. (c) Derive 7, the period in which the Sophisticate goes on vacation. Explain the behavior intui- tively. (d) Explain differences in the behavior of TC and Naif…arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning