Prove or disprove. Let A, B and C be sets. If A x C = B x C, then A = B.

Q: Calculate F SS³ = . (e* sin y, e* cos y, yz²) and S is the surface of the box bounded by the planes…

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Q: Let C be the curve defined by the following system of equations: √x+6y²-2²=0 3y = z

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Q: 2. Let f be a function defined for all real numbers x -uch that f'(x) < 0 and f"(x) < 0. The table…

A: here we will use relation between a function f(x) and its derivatives to find possible value of W

Q: a Orthonormal basis of R² g✓ Isomorphism c Orthogonal Set b Positive Definiteness ✓Nullspace d✓…

A: You have done wrong c, e and j part.

Q: 44 If x = a[cost +-log tan² t dy T and y = a sint, then find at t= - dx 4

A: x=acost+12logtan2ty=asintt=π4

Q: The complementary solution of the D.E. y"- 4y'+ 4y=e²x y =c ex O y =c e?x O y =c e*+ c zte* Oy…

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Q: Find the area of the region enclosed by r = 2 + cos 0.

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Q: 44 if x = 0 [cost += log tan²t) a dy П and y = a sint, then find at t == dx 4

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Q: Calculate the circulation or line integral of the field F around the closed curve C. F = y³i + x²j;…

A: Given the vector field, F=y3i+x2j. Here curve C is the counterclockwise path around the triangle…

Q: Calculate the flux of the field F across the closed plane curve C. F = x²i+y2j; the curve C is the…

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Q: Use the method of undetermiend coefficients to find the general solution of (a) y(³) −3y"+3y′ −y =…

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Q: Using induction on k to prove that n (^) (¹)....("¯ 12 n ´n – rı — · · · - Tk-1 Pk-1) = n! ri!!…

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Q: Question 28 Evaluate. The differential is exact. (π, π, π) (0, 0, 0) O -2 02 O 0 0 1 -2 sin x cos x…

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Q: If Zhang has 3 times as many nickels as dimes and they have a combined value of 200 cents, how many…

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Q: Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −4zi + 4xk and F₂ = −4zi…

A: Given That : Vector Fields are F1→=-4zi^+4xk^ and F2→=-4zi^+1-4yj^+4xk^  To Find : Using the…

Q: Question 2 Find the work done by F over the curve in the direction of increasing t. F = -9yi + 9xj +…

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Q: Question 3 ( Consider the differential equation x²y" - 3xy' + 3y = 2x³ – 3x². x³ are = (a) Verify…

A: x2y''-3xy'+3y=2x3-3x2

Q: -> -->> u, v and w are three non-coplanar unit vectors and a, ß and y are the angles between u and…

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Q: 1. Let = 27-33+ k, (a) Normalize ü (find the vector that points in the same direction as u, but has…

A: We are given the vector v→=2i-3j+k. Our aim is to normalize the vector v, to find a non-zero vector…

Q: Find the surface area generated by rotating the given curve about the y-axis. x = ett, y = 4et/2, y…

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Q: 125 people were surveyed on the types of volunteering in which they participate. They were asked…

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Q: 66 If a,, b, EN for i = 1,2, 3, then c e determinant; 1+x) a₁b₁ 1+ x) 0₂b₁ (1+x) a₁b₂ (1+x) 0₂b₂…

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Q: Use the Divergence Theorem to compute the flux of the field 1 5ye², 36xz, arctan (√)) x² + y² x² +…

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Q: +1 If p is a natural number, then prove that pn +¹ + (p + 1)²n-¹ is divisible by p²+p+ 1 for every…

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Q: Converting a BASE FIVE decimal into BASE TEN. Step by Step. Complete the table below so that the…

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Q: Question 14 Using Green's Theorem, compute the counterclockwise circulation of F around the closed…

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Q: What is the time domain representation of F (s) = (s + 10) (s²-5-2)-¹?

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Q: 4. Let R be an integral domain having field of fractions F (a) Define i: R→ F by i(a) = [(a, 1)].…

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Q: Problem II Consider a linear transformation L₁ R4 → R³ given below and a linear operator L₂ R³ R³…

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Q: Problem separate figures for each. (Each is a subset of R2.) ). Sketch each of the following…

A: To sketch the Cartesian product

Q: z = sinh-15ej2

A: The given expression is z=sinh-15ej2. The objective is to evaluate the value of the given…

Q: Use Right-endpoint Rule with n = 5 to approximate x√x + 2d x√x+2dx to 4 decimal places.

A: To Evaluate: the integral ∫12xx+2dx using right-end point rule with n=5.

Q: is equal to Select one: True False L-¹ { = + 3 s² +9 52 - 1 1 -/- 1 + 36 ²1 1 3 { } s² +9

A: Properties of Laplace transformation

Q: Given the differential equation y"+y=cse²(x) O A particular solution is given by x − În|csc (x) −…

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Q: Question 10 Solve the system of equations. x1 + 3x2 + 2x3 = 11 4x2 + 9x3 = -12 x3 = -4 O (1,-4, 6) O…

A: We solve given system of equations by substitution method i. e.  We substitute value of one variable…

Q: Question 8 Given the differential equation: A y=c,(1+x arctan(x)) +c Ⓡ (1+x2) y + 2xy - 2y=0 The…

A: Recurrence relation of differential equation using power series

Q: Current Attempt in Progress If f (x) x² and g(x) = (x + 2) (x - 1)(x − 3), find all x for which f(x)…

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Q: For a matrix A: -101 0 0 0 10-1 Find the orthogonal complement of Im (TA)

A: Orthogonal complement of the space

Q: Calculate the flux of the field F across the closed plane curve C. F = yi - xj; the curve C is the…

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Q: eff(V x F) · ds where M is the hemisphere a² + y² + z² = 4, x ≥ 0, with the normal in . M Use…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: A Find all solutions (exact form) on the interval 0 < x < 27 Include reference triangles. (write the…

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Q: Consider the planar linear system X' = AX, where -3] A = 3 -2 (a) Find the general solution. (b)…

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Q: 3. Suppose that Eve is able to solve the Diffie-Hellman problem; i.e., if Eve is given two powers g"…

A: Let p be a prime number and g an integer. The DHP is the problem of computing the value of guv(mod…

Q: If the arithmetic progression whose common difference is nonzero, the sum of first 3n terms is equal…

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Q: Consider a Bézier surface defined by the following control net. C₁,1 = (-6,-1,-8) C2,1 = (-3,5,8)…

A: The Bezier surface defined by the control net C1,1=-6,-1,-8  C1,2=1,3,-1       C1,3=-1,-3,-7…

Q: The graph of fis shown. Graph ff and f on the same set of coordinate axes. y=f(x)

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Q: Evaluate the integral [] exp(-5x² − 2xy − 5y² + x)dxdy R2

A: The rule for a Normal density function is fx,μ,σ2=12πσ2e-x-μ22σ2 where the mean of the distribution…

Q: 37. Y (-4,0)(1, 0) 10x < 21 X 40. 3x² +

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Q: ffs, is the arc length of locus of centre of curvature, then show that √√k²q² +k¹². k² ( ds₁ ds…

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Q: 3. Consider the problem of finding the point (s) on the plane 2x - 2y-z = 36 closest to the origin.…

A: The point is on the plane 2x-2y-z=36