Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

Q: Find all solutions of the system of congruences X= 6 mod 7 X =1 mod 5 I =1 mod 3.

A: Use Chinese Remainder Theorem.

Q: Зх — Зу — 6z %3D —3 2х — 2у — 4z %3D 10 2х + Зу + z %3D7 -

A: The equations can be expressed as x - y - 2z + 1 = 0x - y - 2z - 5 = 02x + 3y + z - 7 = 0

Q: 4.30. Compute the real integral -27 do 2+ sin o by writing the sine function in terms of the…

A: To find- Compute the real integral ∫02πdϕ2 + sinϕ by writing the sine function in terms of the…

Q: Solve 6x^5 - 41x4 + 97x3 - 97x² + 41x -6 =0 Solve by reciprocal equation.

A: if an equation remain unaltered on unchanging x to 1/x it is called a reciprocal equation a…

Q: 10. y' -y = x*y%a 3 10. y' – 11. у' + 2ху %3D2х3у3%; у(0) %3D1 12. y' + ху %3D 6х /y 13. y' +y = y-2

A: Multiple :    We have given differential equation ,  y' - 3xy = x4y13 Divide both sides by , y13…

Q: Consider the permutation T = (taqgblvxh)(n sk w fue)(ycodjr)(pzmi). (a) Showing your working, and…

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Q: A) S16 S cos (16r x) dx dy. Osxs 2 Os ys x* B) Find the area between the parabolas x = y -1 and x =…

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Q: Find the centroid of the region bounded by the graphs of the functions y = 4 sin(x), y = 1 and x =…

A: We can find the centroid by using formula

Q: 10 Find the projection of v = -14 onto the -15 -4 -4 3 subspace W of R' spanned by -6 | and 6 - 910…

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Q: (4,28) is a maximum or a minimum point of the function g(x) = -x3 + 6x? – 4. Verify whether the…

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Q: Suppose the region R is bounded by y = 0, y = x, and x = 1. Evaluate: 4.x2 dA =??? 1+x4 R 2.0 1.5 dy…

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Q: How.) Find the absolute maximes and minima far the funCtion (4x-x') Cosy an the Pectangular plate…

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Q: (b) Consider the linear operator on R3 defined by performing the following operations in order: • an…

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Q: Calculate the inverse: s2 +1 L-1 (s – 1)(s + 1)(s – 2)J

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: We define an arithmetic sequence of functions: fn: [1,0) → R recursively as: fi(x) = Vx, Vx € [1, 0)…

A: Given fn:[1,∞)→ℝ recursively as: f1x=xfn+1x=x+fnx for all x∈[1,∞). (a). Let x∈[1,∞), therefore:…

Q: Use forwards, back ward and centered difference approach to approximate the derivative of the f (x)…

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Q: Find the general solution of DE: 4y" + y = 2 sec(t/2), -n <t <n given that the functions y, (t) =…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges giver by the vectors u, v and w is…

A: The given points are P-2,6,0,Q2,1,-3,R1,0,1,S3,-2,3 So            PQ→=4i^-5j^-3k^PR→=3i^-6j^+k ^…

Q: (a) Determine the adjacency matrix A of the graph. (b) Compute A. How many walks of length 3 are…

A: This is a question of Graph Theory.

Q: Solve x3 - 3x² +12 x +16 =0 Solve by cardan' s method

A: cardan' s method  to remove the x^2 term put y = x-(-l/3)  or x = y-l/3

Q: grows grow corn, $6000 to grow wheat, and $5000 to grow soybeans. Because of market demand the…

A: The question has a printing mistake in the number. Solve assuming that.

Q: Consider the permutation (t aqgblvxh)(n skw fue)(ycodjr)(p z m i). (a) Showing your working, and…

A: The complete solution is in given below

Q: Approximate the arc length of the curve y = x over the interval [1, 2] using the trapezoidal rule…

A: Introduction: The length of arc of a given curve over a given interval is another important…

Q: To test for convergence or divergence of the series an, the ratio test computes the limit an+1 R=…

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Q: Give an expression that represents the ratio of the surface area of a cylinder to the surface area…

A: We have to give the expression that represents the ratio of the surface area of a cylinder to the…

Q: A triangle has two of its corners in (4, 0, 7), (0, 4, 7), and the third on the curve in space that…

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Q: 1. Evaluate the principal value of : - j1) (1+ j1)ª 1 O A. 2.808 + j1.318 O B. 2.808 - j1.318 O C.…

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Q: Use the method of variation of parameters to find a particular solution of the differential equation…

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Q: Solve for X(n) using any 2 out of 3 methods of the given X(z). 1 X(z) = (1– z--)(1– z-2)

A: Given z‐transform can be written as Xz=z3z-1z2-1=z3z+1z-12

Q: 1. Determine whether the argument is an example of inductive reasoning or deductive reasoning. Two…

A: This is a question of Logical reasoning.

Q: OA g=0073² - 7 3331 + 724 889 OB. g-0.073-7.7651 + 724 889 OC. g=0434-7333 + 724 889 OD. g=0073 7333…

A: Here is the answer.

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: left Riemann and right Riemann sum

Q: 4. Use Method of Undetermined Coefficient to solve for the general solution of the given…

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Q: Let u be a solution of the wave equation uu - 2u = 0. Pick four distinct characteristic lines two of…

A: Given: The wave equation, utt-c2uxx=0, of which u is a solution. Four distinct characteristic lines,…

Q: 3. Let f(z) = 1-z and y(t) = t+it for t E-1,1). (a) Sketch the image of the curve y. (b) Evaluate…

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Q: Find the exact arc length of y 3 1 over [1, 2]. 4x -

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Q: Question 23 Find the solution. 2y dx = (x2-1)(dx - dy) %3D A (y-1)y (x+1)(cx + y- 2lnly+1|) B (x-1)x…

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Q: 1+a 1 1 1 1+b 1.1 1 + 1 Prove that 1 = abcd 1+ 1 + a 1+c 1 1 1 1 1+d

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Q: i. Look for or create your own linear transformation T: R" → R". where n, and m are both R³, both…

A: In this question, we have to find the examples of linear transformations : (A) T : ℝ3→ℝ3(B) T :…

Q: 3. If laplace f(t) = find laplace f(4t)

A: Given that Lf(t)=1ess to find the Laplace of f(4t) use the linearity property

Q: 5. Compute sin a e + 3e¬z

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Q: Theorem 3. Let A be a bounded linear operator acting between two real Hilbert spaces. Then 1.…

A: Given: A is a bounded linear operator acting between real Hilbert spaces. To prove: 1) R(A)⊥=NA* 2)…

Q: 5. Compute sin a e + 3e¬z

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Q: 5. For the differential equation y" + xy' + 2y = 0 about x, = 0. a. Find the power series solutions…

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Q: A. Find the general solution of the DE: y" - 2y' +y = 6e'

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Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

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Q: Perform each using the polar form of z. 2(V3-i) 3. (1+1)2 Final answer should be expressed in terms…

A: Which is the polar form.

Q: In practice, when comparing two means using small samples, when would you recommend assuming equal…

A: The complete solution is in given below

Q: 2 -1 . Let A -2 3 (a) Find the eigenvalues and corresponding eigenvectors of A. (b) Find a…

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Q: The figure below shows an isosceles triangle PQR, where |PQ|=|PR| and a rectangle ABCD drawn inside…

A: The formula to calculate the area of a rectangle is A=l·w, where l and w are the length and width of…