x = a (t-sint) Cycloid and function placed T the of the in the it be. Using the Theorem we y = a (1 _ cost) aso x-axis Mass bounded by the The density is of the planair plate constant 1 let region second Pappis - buldin determine the center can of gravity of this plate. find it.

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Q: Consider the function f(x) = = x² + 7x + 13 x + 4

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A: Given A = {a, b, c, ..., x, y, z} As Total vowels = 5 Total consonants = 21

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Q: Problem 2.1. Prove that V p() (0, 1). = {v € V(9): v(0) = 0}, is a subspace of

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Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

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Q: Identify and sketch the domain of the function In (4-x² - y²)-√√ √(x−1)² + y² −1 f(x,y) =

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Q: (a) (i) use the definition of C{-} to determine C{te"}. (ii) Evaluate C¹ {}.

A: According to the guidelines I am answering only first question with its parts. (i) Lte4t (using…

Q: (ii) Evaluate L-¹ {,2²9}. [2

A: Sol:- L-12s2+9 =L-123·3s2+32

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Q: a = 3.5 in. 6 in. 2 in., Part A 1 in 1 UR in. 1 in. Determine the distance x to the centroid for the…

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Q: The function f(x) = 2 * sin(x) − e/4 - 1 is zero for two values near x = -5. Use bisection to find…

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Q: a) Sketch the region enclosed by y = 1/x3/2, to the right of the line x = 1, and the x- axis. b) Set…

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Q: X Y Z' WXXN W. Y ED O XYZ' + XY + WX'YZ (XYZ)+(X+Y) + WX'YZ F

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Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

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Q: 1 ? < 40. The cubic x³ - 2x² - x + 1 has three real roots; one is negative. a. Find a rearrangement…

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Q: 4. Determine if the following statement is true or false. Theorem 1.2.1 in your textbook (Existence…

A: Solution 1: dydt=ty, at (1,1) Let  f(t,y)=ty Now ∂f∂y=-12ty32 Now ∂f∂y=12ty32 At point (1,1) ∂f∂y≤12…

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Q: Find the centroid of the plane area bounded by the parabola y = 6x - x² and the line y = x

A: To Find: The centroid of the plane area bounded by the parabola y=6x-x2 and the line y=x

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Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

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