1. Use Stokes'theorem to evaluate fF.dr where F = z²î + y² + xk and C is the triangle C with vertices (1,0,0), (0,1,0) and (0,0,1) with anticlockwise rotation.

Q: Which is the definition of a transitive relation? 2 x~y⇒y~x for all x, y E X. x~y and y~ x⇒x~z for…

A: Transitive relation

Q: Let F, L, K be fields such that K/F is Galois and FCL C K. Then prove or disprove that : (i) L/F is…

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Q: An oil spill is being treated by microbes which eat the oil molecules such that the oil…

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Q: Let R be the set of all real numbers and let a * b = denotes * be a binary operation on R, given by…

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Q: Suppose that f(x, y) = x + 4y on the domain D = {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4}. D a Then the…

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Q: dy 1) Solve the initial-value problem x² - 2xy = 3y¹ with y(1)=1/2. dx

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Q: A (ii), (iii) (i), (ii) B P (1) (iv) Suppose f: A B is a non-zero group homomorphism. Which of the…

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Q: Solve the simultaneous system of congruences: 3x = 7 mod 11 5x 10 mod 15

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Q: 3. Let where (a) (b) Calculate (c) ( (e) Calculate F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = y 0 if x…

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Q: For any prime p, show that there are no homomorphisms between F 2 and F 3 field P p in either…

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Q: Let T₁: V₁ Consider the following questions. A. Prove that if T₁ and T₂ are both one-to-one, then so…

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Q: Given magnitudes w, x, y, z, Euclid defines w: x <y: z as: there are natural numbers and n such that…

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Q: Consider the following functions f(x) = sin(x) and g(x) = /8 cos(x). (a) Determine the linearization…

A: Linear approximation of the function  y = f(x) at x= a can be written as  L(x) = f(a) + f '(a) ( x-a…

Q: 2) Solve the initial-value problem (x² + 2y²) dy : dx = xy with y(-1)=1.

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Q: dy 1) Solve the differential equation = (x + y + 1)². dx

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Q: Find the volume of the region under the surface z = corners (0, 0, 0), (3, 0, 0) and (3, 3, 0).…

A: To find the volume of the region under the surfaces

Q: Graph the equation y = log3 x on your paper. Clearly label at least 3 points on the graph.

A: We have to graph the following equation  y = log3x

Q: Calculate ru x rv. i COS V -u sin v = sin vi- cos vj + uk ru x r₂ = det j sin v u cos v k 0 1

A: When partial derivative is performed with respect to a specific variable, then all other variables…

Q: Use spherical coordinates to find the total mass M and the moments of inertia Ix, Iy, and I₂ of the…

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Q: Perform the indicated operation and express the result as a simplified complex number. 16+28i (2+6i)…

A: Given, (2+6i)(5-i) Now we multiply (2+6i) and (5-i) So, 2*(5-i) + 6i*(5-i)   = 10 - 2i + 30i - 6i2…

Q: 3.- Let R. be the region bounded by y=x², r=1, and, y = 0. Use the shell method to find the volume…

A: As per our guideline, we are supposed to solve only first three subparts. Kindly repost other…

Q: What is the derivative of the expression: eax²+bx where a=2 b = 3 when evaluated for x=0.181 Give…

A: Derivative of the function

Q: = Find the volume of the region under the surface z = xy² and above the area bounded by x = 12. x +…

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Q: 2) Solve the initial-value problem y¹/2 dy + y3/² = 1 with y(0)=4. dx

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Q: Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings…

A: Here we have given that r=15%=15100=0.15. The monthly loan payments are designed in such a way that…

Q: Solve the system of differential equations -β α -β α -βα α -β α -β -β α -β α d -u = dt α -β u

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Q: Question: Using matrix algebra techniques, find a general solution to the system. x' = 2x-6y y' =…

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Q: SOLVE THE FOLLOWING ODE STEP BY STEP IN DIGITAL FORMAT PLEASE dx d²x dy² +3+5y dy x² + y - 2x = 7…

A: We are given the following equations.             d2xdy2+3dxdy+5y3=2xx2+y-2x=7 Let us first solve…

Q: From the following equations identify if they are ODE, the dependent and independent variable as…

A: An equation which involves derivatives and there is a relation between dependent and independent…

Q: 2. Solve the initial-value problem (x + y)² dx + (2xy + x² − 1)dy = 0 with y(1)=1.

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Q: 3. 29 a) XZ = 91 13 cm P 292 b) AC = 2° c) PC = √3 L 13 21 cm Given AACP = ALNX, find each missing…

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Q: APPLICATIONS 3. A pressure gage for a boiler allows the boiler to run as long as 3(x+5)-1…

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Q: Solve the differential equation dx = 1-x-y x+y

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Q: The rectangular bird sanctuary with one side along a straight river is to be constructed so that it…

A: Let y be the length of the river and x be the length of the adjacent side Given that total area is 8…

Q: Let R be the set of all red things Let A be the set of all apples Let B be the set of all bruised…

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Q: Question Analyze the following graph of f'(x). Select all of the intervals over which f(x) is…

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Q: Given the tetrahedron with vertices (2,0, 0) (2, 4, 0), (0, 0, 0), and (0, 0, 4), set up but DOT…

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Q: 8. If necessary, express each equation in point-slope form, then graph each equation on the grids…

A: The graph of a function is the ordered collection of points (x,y) in the cartesian coordinate system…

Q: 6. Let R to be the region bounded by y-axis, a curve y = 2², and a line y = L. (a) (**) Find a, b,…

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Q: Let where (a) F(x, y) = P(x, y)i + Q(x, y)j. P(x, y) = y 0 -y Determine whether if x > 0 if x = 0 if…

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Q: 9. For each of these collections of premises, what relevant conclusion or conclusions can be drawn?…

A: We need to determine the conclusion from given collections from premises. Here are some rules of…

Q: Show the following functions are holomorphic on the domains given, and compute their derivative…

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Q: In questions 6 through 10, determine if the alternating series is convergent or divergent. Which…

A: We are given the series  ∑n=1∞(-1)n-1n2n+3 And the series  ∑n=1∞(-1)narctan(n) We have to check if…

Q: Let G be a group of order 75. How many Sylow p-subgroups can G have, where p = 2, 3, 5 ? Further, is…

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Q: Consider point P(x, y) in first quadrant. Its reflection abou x-axis is Q(x₁, y₁). So, x₁ = x and y₁…

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Q: element-chasing argument to show that: Use an For all sets A, B, and C: If (A U B) ≤ C, then (AB) =…

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