Duplication of answer script(s) will lead to equal sharing of mark among student

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Duplication of answer script(s) will lead to equal sharing of mark among students involved. Please solve on your own effort. Please ensure you have signed assignment submission sheet upon your submission. In a room containing 20 000 ft3 of air, 600 ft3 of fresh air flows in per minute, and the mixture (made practically uniform by circulating fans) is exhausted at a rate of 600 cubic feet per minute (cfm). What is the amount of fresh air y(t) at any time if y(0) = 0? after what time will 90% of the air be fresh? In a bimolecular reaction a + B rightarrow M, a moles per liter of a substance B are combined. Under constant temperature the rate of reaction is y 1 = k (a - y) (b - y) (Law of mass action); that is, y 1 is proportional to the product of the concentrations of the substances that are reacting, where y(t) is the number of moles per liter which have reacted after time t. Solve this ODE. assuming that a b. let m = 2, c = 6, k = 27. and r(t) = 10 cos t For what will you obtain the steady- state vibration of maximum possible amplitude? Determine this amplitude. Then use this and the undetermined-coefficient method to see whether you obtain the same amplitude. Even and Odd Functions, (a) are the following expressions even or odd? Sums and products of even functions and of odd functions. Products of even times odd functions. absolute values of odd functions. F (x) + f (-x) and f (x) - f (-x) for arbitrary f (x) (b) Write e k x. 1 / (1 - x). sin (x + k). cosh (x + k) as sums of an even and an odd function. (c) Find all functions that are both even and odd. (d) Is cos 3 x even or odd? Sin3 x ? Find the Fourier series of these functions. Do you recognize familiar identities? Explain mathematically (not physically) why we got exponential functions in separating the heat equation, but not for the wave equation. The edges of a thin plate are held at the temperature in the sketch. Determine the steady-state temperature distribution in the plate. assume the large flat surface are insulated. The Laplace transform of a piecewise continuous function f (t) with period p is L (f) = 1 / 1 - e -ps e - st f(t) dt (s > 0) Prove this theorem. Hint: Write = + Set t = (n -1) p in the nth integral. Take out e - (n-1) p from under the integral sign. Use the sum formula for the geometric series. L (f) = 1 / 1 - e - ps e - st f (t) dt

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please dont ask so many questions just for 350 KP! be a bit more considerate.

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