4. Let f(x, y, z) = e²x + √y-2², with x = rsinh ¹(st), y = 38²4-¹ and af by using the chain rule. Hence, give your answer in √t Z Find r at term of r,s and t.

Q: 3. Suppose that p and q are odd primes. Show that pq is a pseudoprime base 2 if and only if ord,…

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Q: Which of the following transformations are linear? Select all of the linear transformations. There…

A: Note: As per our guidelines, we can solve the first three parts. Please repost the remaining parts.

Q: 4. Let X be a metric space. Show that if every continuous function f : X → Ris bounded, then X is…

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Q: D. Find (with proof) the infimums of the sets S = {1/n: n = N+) and T = {(-1)" /n:n € N†}. Is either…

A: and To find: Infimum of the given sets.

Q: H E B D A F Find any Euler circuit on the graph above. Give your answer as a list of vertices,…

A: Given: A graph having  vertices and  edges.To find a Euler circuit for the above graph.Concepts…

Q: Use a power series to approximate the area of the region with an error of less than 0.0001. Use a…

A: Given information:The integral .To find:The approximate area of the region using a power series with…

Q: Factor x4 1 completely in R[x] and then factor it completely in

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Q: 1) If A = 35 01 (49) and B-(4) -4 2 -6 Find:- a) BA b) |B| = c) Adjoint A d) B-1

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Q: a) If the initial data uo is a bounded, compactly supported function then show that t lution u…

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Q: The figure below is the graph of a sinusoidal function C(x) with midline y = 6 and a minimum value…

A: Given that the graph of a sinusoidal function with midline anda minimum value of 1.…

Q: Let G be a graph. Prove that G is Eulerian if and only if G has an orientation D where D is an…

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Q: ·0-0-0 6= Az = 6, where A = How many least-squares solutions does this system have? (A) 0 (D)…

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Q: for a fixed n>1 Show that all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

A: To Proof: For a fixed n>1 , all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

Q: 3. Consider the function f (x, y, z) = sin(y) - √x² + z². (a) (b) ( (2, 1, 1). ) Find the gradient…

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Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

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Q: Write down the 4 x 4 rotation matrix that takes the orthonormal 3D vectors u (Xu, Yu, Zu), V = (xv,…

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Q: Required information Employ the events feature of the solve_sp function to determine the period of a…

A: Given that the simple linear pendulum with the initial condition θ=π8.Let us consider the length of…

Q: Two vertical poles are crected 3 meters apart. One pole has height 1 meter, and the other pole has…

A: Let AB and ED be the poles and BD denotes the distance between them. ACE be the string.(The figure…

Q: Use the simplex method to solve the linear programming problem.Convert linear equations by using…

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Q: Determine how many times the innermost loop will be iterated when the following algorithm segment is…

A: The objective of the question is to determine the total number of iterations of the innermost loop…

Q: Consider the following model: Xn+1 = 1.039xn - 0.0003xnYn Yn+1 = 0.88yn + 0.0001xnYn Where X = the…

A: Let Xn=F(Xn) where Xn=[xn,yn]T be a system of difference equations , then the equilibrium occurs at…

Q: Let f: R → R³ be defined by ƒ(x) = (1, 6x², 3x). Is ƒ a linear transformation? a. f(x + y) = f(x) +…

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Q: Construct the Taylor series for f at x0=0.

A: We need to construct the Taylor series for f at x0=0.

Q: Problem #2: Consider the following matrix A and column vectors K₁, K₂, and K3. Problem #2(a):…

A: Given that    The eigenvectors of A are        Let  are corresponding eighenvalues of A. Then…

Q: . (i) Show by hand that 2 is a primitive root mod 19. ii) Find2 a complete set of primitive roots…

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Q: Let 3 A = -1 -1 3 -1 -1 3 (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = P-¹AP…

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Q: Represent the function Co Compute the first few coefficients of this power series: C1 C2 C3 CA || 5…

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Q: .,Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace…

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Q: Letf : R² → R be defined by f((x, y)) = 8x + 5y + 1. Isf a linear transformation? a. f((x₁, y₁) +…

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Q: 5. f(x, y, z) = x z=1-x² X ZA y+z=2 E y

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Q: 19. As in Exercise 18, calculate A¹0x for 1 2-1 05-2 6-2 A = 0 and x = 2 4]. 7

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Q: A given by 1. M₁1 4. M41 12. A = 14. A = 16. A = A = 2-1 3 1 4 13-1 624 1 2 20-2 2. M₂1 5. M34 12 4…

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Q: Solve the boundary-value problem y" − 8y' + 16y = 0, y(0) = 3, y(1) = 0. y(x) = help (formulas)…

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Q: If T:P1→P1 is a linear transformation such that T(1+4x)=−1+2x  and  T(5+19x)=4−2x,  then T(−2−4x)=

A: Let  T:P1 to P1 is a linear transformation     T(1+4x)=-1+2x      T(5+19x)=4-2xClaim : find T(-2-4x)

Q: ۲-'{ (5 + 4 ) 3 ? 4 S

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Q: 5. Find an orthonormal basis for the subspace of R³ given by {(x, y, z)T : x − y+ z =0}

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Q: Let f: R → R³ be defined by f(x) = (7x, 7x, 2x). Is ƒ a linear transformation? a. f(x + y) f(x) +…

A: We have to check  is linear transformation or not.

Q: H.W Find the Laplace Transform of Find L sin h2tdt [te™ sin tdt 0

A: Here we have to find the laplace of two given f(t).

Q: Use the compound interest formula to determine the final value of the following amount. $1800 at…

A: Principal(P)  = $ 1800Rate of Interest(r )  = 11.2%Time = 2.5 yearsHere first we take n = 2 years.A…

Q: TB Consider the ordered bases B = [M]B = -3 4 (8 96382)- 0 0 -2 -3 1 0 4 2 c=3² 39.6 * 3) ) for the…

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Q: Part II. Writing the equation d² dt² in the form of the system x= x= x², x = V₁ v = x= x² dt = x(t),…

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Q: Find the inverse of the rigid body transformation: R t 000 1 where R is a 3 x 3 rotation matrix and…

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Q: 3. Display an argument to show that the Gamma Function is defined for s> 0. T(s) = f e-¹4³-1 dt. 0

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Q: Let P, denote the vector space of polynomials in the variable æ of degree n or less with real…

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Q: Let f: R → R³ be defined by f(x) = (x, 6x², 3x). Is ƒ a linear transformation? a. f(x + y) f(x) +…

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Q: Let P, denote the vector space of polynomials in the variable a of degree n or less with real…

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Q: Part II. Writing the equation d² ; =r_r dt2x in the form of the system v² d dt x = v, v=x-x² W(x): =…

A: Let md2dt2x=F(x) be a differential equation,  then the conservative quantity is given by…

Q: Which of the following transformations are linear? Select all of the linear transformations. There…

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Q: Consider the direction field below for a differential equation. Use the graph to find the…

A: Given that:       We have to find the equilibrium solution using this graph.

Q: Find the general Solution For D. E y + y tanx [cos²x]y¹

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