2. A cone of radius 2 cm and height 5 cm is lowered point fırst into a tall cylinder of radius 7 cm that is partially filled with water. Determine how fast the depth of the water is changing at the moment when the cone is completely submerged if the cone is moving with a speed of 3 cm/s at that moment.

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Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

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A: To find- Sketch the region R of integration and switch the order of integration. ∫110∫0lnyfx, y dx…

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Q: nd a basis for the set of all vectors of the form below, where a, b, c are real numbers. [ a-2b+5c,…

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A: Given function is Fs=4s+2s2+2s+5

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Q: Solve for the general solution of the equation: 2y’’ + 4y’ + 200y = 0. Show all math steps.

A: Here we use basic Auxillary equation to solve this

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A: Given integral is ∫9t + 8tdt

Q: Exercise 14.3.34. Compute each of the following. Note that e.g. (123)2 means the same as (123)(123).…

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Q: (1) Determine whether or not the function u(t) = sin(2t) + cos(2t) is a solution to the differential…

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A: We solve the given problem by method of saperation of variable.  In this method we consider the…

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Q: Solve the initial-value problem y"(t) – 4y'(t) + 4y(t) = 4e2t; y(0) = –1, y' (0) = –4.

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Q: Is it true that when an n*n matrix whose columns form a basis of R^n, then A is invertible?

A: We shall answer this in next step

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A: Solution: Given that

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Q: 5. Triangle ABC is a right triangle with an angles A = 90°, B = 36.86°, and C = 53.13°, If AC is…

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Q: Use the Newton-Raphson method to find the roots of the function f(x) = e-0.5x(4 - x)-2. With the…

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Q: Prove that If k, q, w and r are integers, and if c|k and c|q, then c|(kw + qr)

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Q: 1. Construct a Turing machine that accepts L = {0"1"0" | n > 0}

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Q: 1 1 0 3 1 and b -3 5. Let A = Show that the linear system Ax = b is inconsistent -1 0 0 -1 1 -2 4…

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