Q-2 Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°c. At t=0, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t), where x is the distance from the left end of the rod, x=0. The U(x,t) is a solution of the initial boundary value problem: U, = « Ugx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 30, 0

ii) Find the value of a, correct to two decimal places, such that Pr(Y s a) = 0.7

Suppose that a particle moves along a straight line with velocity cos(t/2) , sin(t/3), te [0, 7], t E (T, 37], v(t) = %3D in meters/second. What is the total distance traveled from t = 0 up to t = 3T seconds ? (You only need to input %3| Type your answer..

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The acceleration of an object (in m/s²) is given by the function a(t) = 9 sin(t). The initial velocity o object is v(0) = -6 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = −9 cos (t) + 3 b) Find the object's displacement (in meters) from time 0 to time 3. 5.8584 X meters c) Find the total distance traveled by the object from time 0 to time 3. 16.7176 X meters

Automobile traffic passes a point P on a road of width w feet with an average rate of R vehicles per second. Although the arrival of automobiles is irregular, traffic engineers have found that the average waiting time T until there is a gap in traffic of at least 1 seconds is approximately T = te Riseconds. A pedestrian walking at a speed of 3.3 ft/s requires t =s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is f(w, R) = () WR/3.3 What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second? (Use decimal notation. Give your answer to two decimal places.) (= Use the Linear Approximation to estimate the increase in waiting time if w is increased to 26 ft. (Use decimal notation. Give your answer to two decimal places.) Af = 31.15 t = Estimate the waiting time if the width is increased to 26 ft and R decreases to 0.18. (Use decimal notation. Give your answer to two decimal places.) 6.37 A = 32.48 Incorrect What…

12. What is the equation of horizontal axis of the function f(x) 2(3 sin x +2)? a. y = 6 b. y = 3 С. У 3D 2 d. y = 4 %3D