1. Find a vector valued function that represents the curve of intersection of the semi-ellipsoid x² + y² + 4z² = 4, y ≥ 0, and the cylinder x² + z² = 1.

Q: Consider the following functions. f₁₁f₂ R² OR + S₁ (x₁, x₂) = x² sin(x₂) + X₂ exp(x₁) 12 (X₁1×₂) =…

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Q: Solve the system of equations 3 dx 2 dy -x+y=t-1 +2 dt dt dx dy dt dt + -x=t+2

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Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: To extract more information out of the graph we will try to match the traces in the following order…

Q: 24 A figure is shown. (-2.7) (-2.1) (2.7) (2.1)

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Q: Let X be a continuous random variable with a uniform distribution in the interval [0, 1], i.e., X ∼…

A: The transformation of a random variable involves creating a new random variable through a function…

Q: 6 B *- {[1][*]} [6]. -- 6 [3] is an orthogonal basis of R². Find [v]®•

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Q: Q3. Let A be a 6 × n matrix of rank r and let b be a vector in R6. For each choice of r and n that…

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Q: In general given two matrices A and B then: A' = B'. O None of the other answers. ○ A'B = (B' A)'.…

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Q: This question is about matrices in M₁ (K) for a field K. (a) Is it true that two similar matrices…

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Q: 5. (a) Show that logi() = log M — log N₁ where M, N>0 and b>0 and b ‡ 1. log, M where M>0, b>0, c>0…

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Q: y" - 4y" - 5y = Cosh X solve the following ODE please step by step

A: Note: The given differential equation   is not correct.By assuming  , we solve this differential…

Q: 2. Suppose that c₁,C2,C3,... is a sequence defined as follows c₁=0, c₂=-10, c3 = 10³ and Ck=11ck-3…

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Q: Consider the two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

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Q: 6. Solve the following problem for u(x,t): ²u du Əx² Ət = subject to the conditions u(2,1) = 1,…

A: The given partial differential equation (PDE) is a heat equation, and you are also provided with…

Q: (d) Find a unit eigenvector, v2, for eigenvalue A₂. (e) Construct a matrix P such that A = PDP-¹ = P…

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Q: Given basis = {QOB]} {[ 2 5 3 {C₁, C2, C3}. find the basis C = of R³ and change of basis matrix [B]C…

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Q: Show the vector field V = (8xy³ z, 12x²y² z, 4x²y³) is irrotational, and find its potential. Then,…

A: To prove that the vector field is irrotational, we prove that the curl of the vector field is zero.…

Q: mol K 1) The Ideal Gas Law, PV = RT, relates the pressure (P, in pascals), temperature (T, in…

A: Given the relation between volume, temperature, and pressure by the Ideal gas law as .(c)Consider…

Q: Particular values for the function f(x) are given in the table below. X f(x) 9 18 Use the table to…

A: 918273645-9-15-20-19-6We hae to find:(a) a right-hand Riemann sum(b) a lift-hand Riemann sum

Q: Find the work done by the force field F(x, y) = x sin(y) i + yj on a particle that moves along the…

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Q: c) d² y dt² +2 dy dt + y = 4t, y(0) = 0, y'(0)=5

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Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -15 -32 -18 12 -56…

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Q: 8. Si 0. si xo < 0. si xo = 0

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Q: 1-Find the cosine of the angle between A and B with respect to the standard inner product on M22 2 4…

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Q: cos - sin 0 0 where x, y, and z are distinct. sin cos 0 0 A: 0 0 cos - sin 0 0 sin 0 cos and B 1 x…

A: For a square matrix of order n×n , the greatest integer r ≤ n , such that there is at least one…

Q: To R¸(ß) = b² lim # To → To 0 sin(@₁t+ ) sin[@₁(t− B) + ]dt

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Q: 3. Let the function f be defined by for - < x < π and satisfy f(x + 2π) = f(x). Recall that cosh x =…

A: 3. Let the function ƒ be defined byf(x) = cosh(x)for -  &lt; x &lt;  and satisfyf(x + 2) = f(x) .(a)…

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

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Q: 3. Show that Z10 is isomorphic to Z2 × Z5, but that Zg is not isomorphic to Z₂ × Z4.

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Q: Which of the following is the best estimate of f f(x)dx where f(x) is given in the figure below? (x)…

A: The area of rectangle is given by length x breadth

Q: Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select…

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Q: F(s) = s+1 2 S² - 2s+2

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Q: 3. Show that (a) (4²)C = A (b) A-B=An Bº (c) AN (BUC) = (ANB) U (ANC), (d) AU (BNC) = (AUB) n(AUC)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: [X₁ + x₂ + x3 x4 3x1 +5x22x3 + x4 -3x₁7x₂+7x35x4 1+3x2 - 4x3 + 3x4 = 3 = 1 = 7 = -5.

A: The given system of equations

Q: Suppose y=f(x) is an odd function. If Sº3 f(x) dx = 5 and 7 f f(x) dx = 12, find the value of 17…

A: Given,  is a odd function,i.e . and We have formual,  .If interval  can break into finite…

Q: Let B = {b₁,b2} and C = {C₁, C₂}. Find [v] and [v]. 10 -9 -8, -6 --5 C/ -4 -3, -2 6+ 4 3 2 1 H -2 -3…

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Q: Investigators evaluated the effect of education (E1=1 if college or more, E2=1 if Masters degree or…

A: From the question the value of A = 35 and M = 1Since the person only has a college degree we can…

Q: below is a python code for solving a system of non-homogeneous linear differential equations. Write…

A: The objective of the question is to plot the solution functions h and v obtained from the given…

Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹ +4 c) f(t) = est sin(3t) e)…

A: Let Then Result:

Q: b) L[4t +5te* +sinh(5)]=

A: We need to find

Q: Question 3.2. dr. (1) Let a, b € R be non-zero. Use integration by parts to determine faze d (Note:…

A: integration by parts:  If u(x) and v(x) are two functions then…

Q: 5. Solve Uzz - 3Uzt - 4Utt = 0, U(x,0) = x², U₁(x,0) = e. Hint: factor the operator as it was done…

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Q: A given scenario of a person falling from a height into a pit attached to a rope can be modeled by…

A: The objective of this question is to find the parameters that would ensure the safety of bungee…

Q: X 1+x² List the elements of the requested image or preimage. No set notation needed. Let q be the…

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Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

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Q: and the SUD of the following am A= 11 94040 220

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Q: Do not Claim ( For all real numbers a, b, c, and do if a = (b +c+d)/3, then either (2b + c) ≤3a, or…

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Q: (d) cation. [11] =2 Write out eigendecomposition of A and verify it with the matrix multipli- m,

A: Eigenvalue decomposition:A=QDQ−1Where the columns of Q are the orthonormal eigenvectors and the…

Q: . Let f:R" →R be a differentiable convex function. Consider the following problem: (P) min f(x) s.t.…

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Q: Exercise 10.1.2 Consider the following functions T: R³ → R2. For each function T, show that T is a…

A: The given functions,(c) (d) The aim is to show that the map  is a linear transformation and matrix…