Given f(x)=√x-5;x#5 and g(x)=x+3. Find the domain of (gof)(x)? All real numbers greater than 5. All positive real numbers All real numbers except 5. All real numbers.

Q: Find the Laplace transform of the following: 1. 4t + 12

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Q: For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. A = -10-17…

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Q: Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e., b M₂ (R) = { [ a &] |…

A: The given matrix is M2ℝ=abcd: a,b,c,d∈ℝ To find : (a) M2ℝ is a ring under addition and…

Q: 2. If f(x, y) = x² + xy − cos(xy), find the domain and range.

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Q: 4. Is M₂ (R) a field? Justify. I 5. Show that T = = { [ ² ] 12,9₁² € R} i 2 is a subring of M₂ (R).

A: Subring of a ring

Q: 8 (i) Σ n=1 Test for convergence the series 3.6.9 ... 3n x" (x>0), 7.10.13... (3n+4)

A: Test for converges of the series, using Ratio test

Q: Let p and g be continuous functions in an open interval I and ão E I. Show that if Yı and Y2 are any…

A: If y1, y2 are any two solutions of dydx+p(x)y=g(x),    y(x0)=y0. where p and g are two continuous…

Q: Let S₁ be the hemisphere with Cartesian equation z = 6 - 36 – x² - y² and S₂ be the upper nappe of…

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Q: Industry Sectors Service Trade and Transporation Total sector United States Total Employment 68%…

A: Percentage change for Services: Percentage for 2010 is 68 and for 2020 it is 69% Hence Percentage…

Q: Referring to the figure, suppose that fo F. dr = 2n fo F. dr = 5n - Use Green's Theorem to determine…

A: Given- Referring to the given figure, suppose that ∮C2F·dr = 2π∮C3F·dr = 5π To find- Use Green's…

Q: Drag the three points so they simultaneously follow both a LINEAR pattern and an EXPONENTIAL pattern

A: Consider the three points (0, 0), (1, 1) and (-1, -1). They follow the linear pattern y=x And also…

Q: Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that:…

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Q: Using the definition of Laplace transform, what is the equivalent integral if f (t) = 5t? Oe at

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Q: Find the Laplacian of the following scalar fields and compute the value at the specified point. (a)…

A: The Laplacian of the following scalar fields are calculated and the value at the specified point is…

Q: Three vectors A, B, and C are related as follows: AB = 22180°, A + C= -5 + 15i, and C is the…

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Q: Find the laplace transform of f(t) = 5t³ - 4t² +8 OF (S) = -8s³ +8s+30 OF (s) 8s³-8s+30 -88³ +88-30…

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Q: Evaluate the following integrals. 4x+10 1. S dx (x-2)(x-1)²

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Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: Let z = g(x, y) = x² + xy³ -y - 6x - 2y +4, where x = r cos (8) and y = r sin(8). дz Use the chain…

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Q: 1. Determine whether the series ż 1 2n+1 1 2n-1) converges or diverges by examining the

A: Given series is ∑n=1∞12n+1-12n-1

Q: Which statement below best describes the graph? 8 6 A X +2+ -4 -6- O Domain = {-4,-3, 0, 2, 7);…

A: We want to find domain and range of given graph.

Q: Evaluate the following integrals. *x*+5x x*+5x³+20x+16 2. x(x²+4)² dx

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Q: Find the line y = a + bx which best approximates the data points y = (-4, 59), (-3,49), (-2, 38),…

A: We have to find the best fitted curve from the given data.

Q: A company can buy a machine that is expected to increase the company's net income by $30, 000 each…

A: Given:   The net income is = $30,000

Q: Find the volume of the solid in the first octant by bounded by the plane 3x +42 = 12, y = 2 and the…

A: Volume bounded by thefirst octent

Q: Page 3 3. For |2 <1, 1+z+z²+... 2 Using this expansion, by matching terms show that if f(2)==0a, 2³,…

A: We have to find maclaurin series for g(x).

Q: 4. Determine whether or not the following are Reflexive, Symmetric and Transitive. (a) on Z: (a, b)…

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Q: Consider the parametric curve C given by X= √x= √2+ - cos t 2y = soin't where te [0.2π] (1)…

A: (1)Given,x = 32t-cos(t)y=5sin2(t)    where    t∈0, 2πcurve C has horizontal tangent line where dydx…

Q: Find the formula 1 [ f(x) dx = w₁f (0) + w₁f (1) that is exact for all functions of the form f(x) =…

A: Solution :-

Q: Transform: F (s) 18-16 s²-08-13 Of(t) = 4e 3 sin2t – 4e-3t 31 cos2t O f(t) = 4e³t cos2t 4c sin2t O…

A: Given: F(s)=4s-16s2-6s+13 To find the inverse Laplace transform.

Q: (a) Determine whether the permutation 42135 of the set {1, 2, 3, 4, 5} is even or odd. (b) Find all…

A: The given permutation is 42135. The given permutation is a cyclic form of the set {1,2,3,4,5}. The…

Q: Solve the differential equation below using series methods. (-7x²+8)y'' - 2xy = 0, y(0) = 4, y'(0) =…

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Q: Find the general solution of each of the following partial differential equations 9uxx-21Uxy + 49Uyy…

A: Find the general solution of each of  partial differential equations  9uxx - 21uxy + 49uyy = 0

Q: do 4. Solve the recurrence relation an+1 = 7an-10an-1, n ≥ 2, given a₁ = 10, a2 = 29. -8an-1-an-2,…

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Q: 3, i,A garden is rectangular being 22 m wide and 45 m long. How long is a line drawn from one corner…

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Q: Consider the plane P with the Cartesian equation 7x+5y + 5z = 33. a) Express the above Cartesian…

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Q: Determine a region of the xy-plane for which the given differential equation would have a unique…

A: Rewrite the given differential equation. y'=x24-y2             ...1

Q: Use three-point midpoint formula to evaluate the first derivative of y=x2+5x−1y=x2+5x−1 at x=0x=0…

A: Given function is y=x2+5x−1. We have to evaluate the first derivative of y=x2+5x−1 at x=0 using a…

Q: Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path…

A: We have to calculate the following integrals i∫C1z2dz  and ii∫C2z2dz where C1 and C2 are given…

Q: Let A Mn(C) be a Hermitian matrix. &

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Q: Find the differential dy of the function y = 4 sin (2x). Provide your answer below: dy=dx

A: Solution

Q: X1 - 3Х2 - 4 X3 = 1 -X1 + X2 - 3x3 = 14 X2-3x3=5

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Q: The revenue of a company making the TV show "It's always sunny in Philadelphia" can be represented…

A: At break even total profit will be zero  To maximize total profit we can use calculus  For relative…

Q: Find the volume of the region defined by the vectors. -21 000 9 5 7 |> 5 Volume

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Q: [34] Find the Laplace transform of f(t): = t² 2t - 8 2 te-2t t 6.

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Q: INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→R - {} defined by f(x) 3x-5 = is bijective.…

A: We have f:ℝ--12→ℝ-32 defined by fx=3x-52x+1 We need to check one-one and onto. If a function is…

Q: 6. Consider the following linear system of differential equations: dY [ -1 5 2 1 Y. dt (a) Determine…

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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…

Q: Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace W…

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Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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