A line intercepts the x-axis at x = 3 and the y-axis at y = 8. What is the equation of the line?

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Q: 5) (x + y)dx + (x + 5)dy = 0 (Exact).

A: Exact differential equation.

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Q: Consider the polar curves Cı : r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

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A: Please look into the next step for detailed answer

Q: What is the Laplace transform of the given differential equation? O 2 (3-2) s+1 O 8² (8-2) 07²-25…

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Q: 1) Are the following functions analytic? a) f (z) = z z b) f(z) = z + z2

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Q: 6. Sarah prepares a side dish of peas and carrots to bring to her family potluck lunch. The recipe…

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Q: Find the general solution of the given differential equation. dy y(x) = x35-x3 + Cx2 Give the…

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Q: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is defined by R= {(x, y) E AXA: x…

A: Here according to the definition,       R = {(x,y) : x = y mod 3} Then if y = 7, then x must be 7…

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y²,1 ≤ z ≤ 4, if its density…

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Q: 1. Consider the mathematical systems (R, *1), (R, *2), and (R, *3) where *1,*2, *3 are defined as a…

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Q: Determine the solution of the equation 2 cos x -0.5√x = 1.

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Q: - In a survey of 500 students of a college, it liked watching hockey and 62% liked watc

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Q: Prove by induction: 1(3) + 2(4) + 3(5) + .... + n(n+2) = n(n+1)(2n+7)/6

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Q: 1. For the matrix A=12²5¹ 7 3 6-12-5, (a) Compute the characteristic polynomial f(x) = det(xI - A).…

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Q: (b) 1 (c) e 1 123. the curves y=-e* and y=In (ax), (where a is positive) has only one point is comm…

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Q: Use the inner product (f, 9) = | f(x)g(x) dr %3D in the vector space CU[0, 1] of continuous…

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Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

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Q: polynomial

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Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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Q: 62. dz, C is |z| = 3 C c z² +4

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Q: 2. Prove the following, using induction: (a) If an+1 = an/(an+1) prove that an = ao/(nao +1) for all…

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Q: Find an orthogonal and an orthonormal basis for 5 1 2 W = Span Spa { ·} 0 2 -2 -4 0

A: GRAM-SCHMIDT METHOD The Gram-Schmidt process (or procedure) is a sequence of operations that allow…

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A: Solutions