Let n be integer. Give a proof by contradiction of the following theorem. "If n³+5 is odd number, then n is even number."

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A: Given: Handwritten text. To Do: Transcribe in digital format.

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Q: 2. Let B = {b₁, b2} be a basis for vector space V. Let T: V → V be a linear transformation with the…

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Q: 5) Find, using Spherical Coordinates, the volume of the solid that is enclosed by the cone and the…

A: Given  Z=sqrt(x2+y2) And x2 + y2 +z2=8

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Q: Consider the equations x² - y² − z³+w² +4 2xy + y²-22² +3w¹ +8 0 = 0. (a) Show that near (a, b) =…

A: Given Data: Let us consider the given data, x2-y2-z3+w2+4=0    2xy +y2-2z2+3w4+8 =0

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Q: On the curve x³ = 12y, find the interval of values of x for which the abscissa changes at a faster…

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Q: 4.). Find the interval of convergence. (Enter your answer using interval notation.) ∞     n = 0 xn…

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Q: Problem 1. Let E be a real vector space, F be a closed subspace of E, and a € E\F. Set d(a, F)…

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DI

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Q: [1 -3 4 Find two different diagonal matrices D and the corresponding matrix S such that A = SDS-¹.…

A: Given: The given matrix is A=1-348. To find: We have to find the two different diagonal matrices D1…

Q: Write the system in vector matrix form: a) b) O d) O < X² 4 1 12 KH KH -21 -e e -21 14 21 -21 4 e² 1…

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Q: Evaluate the line integral (3ry² + 6y) dr, where C is the path traced by first moving from the point…

A: The given problem is to evaluate the given line integral over the given path C traced by moving in a…

Q: d²y dt² - dy 3+ 2y = sin t dt y(0) = 0 y'(0) = 1

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal. (If not…

A: A matrix is diagonal , if the algebraic multiplicity and algebric multiplicity of all the eigen…

Q: 1. Convert each second-order IVP into a system of first-order IVPS. (a) my" + cy' + ky = Fo cos(wt),…

A: Denote: y1=y            y2=y'

Q: Find the volume of the solid below the paraboloid z = x² + y² and above the triangular region R…

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Q: n = 0an(x + 5)n converges at x = −6. At which of the following points must the series also converge?…

A: the center of the given series is x = -5   since the series is convergent at x=-6 then it is also…

Q: Given f(x, y, z)=-30-x-y-z+29, use the total differential to estimate the change in f from the point…

A: The total differential of the function: f(x, y, z) is calculated using the formula: df=fxx, y,…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) : F(x, y, z) = = ze³yx

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Q: On July​ 25, 2019, Marilyn gives stock with an FMV of​ $7,500 and a basis of​ $5,000 to her nephew…

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Q: Bergen bought 130 shares of stock in Nike (NKE) on November 3, 2020, paying $124.59 per share. Nike…

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Q: On the curve x³ = 12y, find the interval of values of x for which the abscissa changes at a faster…

A: For the ordered pair: x, y, the abscissa is x and the ordinate is y. We know that: ddxxn=nxn-1.

Q: Use cylindrical coordinates to calculate: [w x² + y²dV W: x² + y² ≤ 16, 0≤z≤8

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Q: 1. Use local linear approximation of the function f(x): = COS $ (√7.92). COS ㅠ 32x at xo = 4 to…

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Q: Use the age transition matrix L and age distribution vector x₁ to find the age distribution vectors…

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Q: 14. For each x ER let Bx = {(x, y) = R² | y ER}, notice that Bx is a subset of R². Show that B = {Bx…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: 7. Let X be a compact topological space. Let {Ci}iez, satisfy Ci+1 C C₁ for all iEZ+. Show that ni1…

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Q: • Put arguments of functions in brackets (e.g. sin(x) rather than sin x). . Give your answers in…

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Q: Solve the differential equation for the variable U(x, t) given by a²u เอบ at = 2 5,0 0 U(x,0) = 25x

A: Given: ∂U∂t=∂2U∂x2 , 0&lt;x&lt;π , U0, t=0, Uπ, t=0 , U(x, 0) =25x ,  t&gt;0 To find: Solution of…

Q: A spring with a 2-kg mass and a damping constant 2 can be held stretched 2.5 meters beyond its…

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Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: 1. Find the solution of the given initial value problem. 2y!! + 3y + y = 5x² +7 cos x

A: The given problem is to find the solution for the given differential equation.

Q: Elementary Differential Equations (Upvote will be given. Please write the complete solutions…

A: We have to find the general solution of the differential equations  a 4D3-3D+1y=0 b D3+3D2+3D+1y=0

Q: 10z Sketch the region enclosed by y = 5, y = ¹0, and x = 1. Find the area of the region.

A: Given : y =e5x ; y = e10x and x = 1 At x =0, y = 1 for both the functions, so they intersect at…

Q: 1. Find a full rank decomposition of the following matrices 1 2 3 0 021 -1 102 1

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Q: A property is a which remains intact under homeomorphism. We Let Let need to show 'Lindelof'…

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT PLEASE

A: Let X is the discrete topology . Let A is the subset of X with  |A|&gt;=2 Assume that A={a,b} with…

Q: 14. In the diagram, AB = BC = CD. Show that OC = OA+OD. A B C D

A: (1)  Given  AB→ = BC→ = CD→     Now we will prove the given equality by using triangle law in…

Q: For u = x7 . y4 . z9 = әби ?х у2 z3 calculate әби дхду20 3

A: Partial derivative: The derivative of a function of two or more variables with respect to a variable…