Using Stokes's theorem, calculate the line integral is the triangle with vertices (0,0,0), (1,0,0), (1, 1,0) with counterclockwise orientation. F dr, where F = [2y², 3z2, z - z] and C

Q: Example: Let W(t) be the rate at which rain falls on a roof of a house for 0 < t< 3, where W is .1…

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Q: [CLO-1] Use the he O Candida O Candidat O Candidat O Candidate

A: the given data is as follows   15 11 9 5 4   First A C D B C   Second B B C A D   Third  C…

Q: Which of the following statements is (are) false if all vectors are in R"? O None of the statements…

A: Given all vectors in R^n .

Q: The eigenvalues of x2y*-xy'- ày = 0, v(1) = 0, y(e) = 0 ks Hint:[Use only case 3]

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Q: Suppose w =+, x = cos? t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: a (e) Let B = be any 2 x 2 matrix. COs a = U11 (i) Show that there are real numbers u1 and a such…

A: We will use the basic knowledge of trigonometry and matrices to answer both the questions you need.…

Q: O If f (y) > f (x*) for any y in R", then x* is the global minimum. If f (y) > f(x*) with ||y – x*||…

A: This is a problem of multivariable calculus.

Q: 3. (a) Determine the value of coefficient a for which the vector field F = (ayz + 22, 2.02?, 6ryz² +…

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Q: (c) A storekeeper has 60m' available for storage of two brands of mineral, drink X and Y. The volume…

A: We will form a linear programming and then solve it graphically

Q: Fiad Laplace transfunm af the function Shown belowin

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Q: Solve the equation .11 y" +3y' + 2y = x2

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Q: -33 makin 3. 6. -6 Jind A 75 %3D

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Q: ow that the polynomial x° + x³ +1 is irreducible over the field of rationals Q.

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Q: What is the approximate volume of the cone below? 7 cm 10 cm A 70 cm B 183 cm 3 с 549 cm D 733 cm 3.

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Q: the row space and for the column space of that matrix. [1 3 0. 0 0 LO 0 0 1 1 1 6. 4. A = 1 -3 Enter…

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Q: Use Eisenstein's criterion to show that the polynomial x3 –- 3x? + 9x – 10 is irreducible over the…

A: Solution :-

Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

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Q: In hs problem you wil use vanation of parameters to solve the nonhomogeneous equation t'y + 2ty - 6y…

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Q: Derive Newton's formula for divided differences for completion CO JO 11:01

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Q: A school is constructing a rectangular play area against an exterior wall of the school building. It…

A: To find the length (l) and area (A) as a function of width (w) .

Q: What is the connection between the concept of the limit of a sequence and the limit of the function?

A: Solution

Q: R Solve the following 2n order ODE using the method of variation of parameters. y" - 4y' + 4 y = (12…

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Q: d?q, dq (c) at? dt = t2 + 2t F(0) = 4 F'(0) = -2 dx +2x 2 dt (d) F(0) = 0

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Q: 25: Using a suitable Fourier- Series expansion for 0 S x ST: A) Show that: x(n -x) (cos 2x cos 4x .…

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Q: (a) Let G and H be two groups and :G Ha function. Define what it means for to be a homomorphism. (b)…

A: This is the problem of Abstract Algebra.

Q: Consider the differential equation dy = x – dx - 2y, for which the solution is g(x). Which of the…

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Q: 1 (a). 22 + 3 (b). (c). z2 – 2' 2 – 22

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: Consider the surface x2 + y2 − 2xy − x + 4y − z2 + 4 = 0 at the point Po (2, −2, 5). Determine the…

A: This is a multi-variable calculus.

Q: 0.2 0.4 0.8 1.0 1.4 1.6 1.8 2.0 1.2 f(x) 1.000 0.916 0.836 0.0741 0.624 0.224 0.265 0.291 0.316…

A: Make Newton's divided difference table and use the divided difference formula to determine the…

Q: obtain the ualues of at x=0,1, o.2 using R.K method of fourth order Por the differential equalion…

A: (1) :- given differential Equation  y'=-y,  y(0) =1  We have to find value of y at 0.1 and 0.2  Take…

Q: (CLO-1] An election involving 6 candidates and 40 voters is held, and the results of the election…

A: We know, a candidate will receive the minimum points by being ranked last on each ballot.

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find The volume of the solid in the first octant bounded by the coordinate planes and the plane.

Q: Using a specific method, your calculated density of aluminum is d1 = 2.74 g/cm3. Using a different…

A: Solution

Q: 2/ Let fcantinous appicatiom Prove thet Fles sf)/BE then SePose fcef) and Proye fis continates a ff…

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Q: y' – 3y = e3t, y(0) = 1

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Q: sin az sin z Given that J3/2(z) = V= - cos z compute cos az dz, where a az is a zero of J3/2(#).…

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Q: 1. Solve the ordinary differential equation, dy z+zy? dz

A: Let us solve the Ordinary differential equations in the next step.

Q: Find the required limit or indicate that it does not exist. 1. lim3(2(t – 3)²i – 7t°j) 2. lim→1(i -…

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Q: Solve the system of linear equations using Crout's LU Decomposition. 11 -10 -2 2 1[X1 Xx. -11] -1 7…

A: To solve the system of linear equations using Crout's LU decomposition method. Given that…

Q: Let I be the 6 × 6 identity matrix. What is the geometric multiplicity of its eigenvalue? Answer:

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Q: Find the inverse transform of the given functions: 2s2-6s+5 1. F(s) : (4s3-8s2+6s-1 )(s²-4)

A: Here, we need to find the inverse transform of the given function.…

Q: Give 5 sample word problems for Orthogonal Trajectory (Application of Differential Equation).…

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Q: Calculate the value of the error with one decimal place for: z = x/y where x = 6.2 +/- 0.3 and y=…

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Q: Perform the Gram-Schmidt process on the following sequence of vectors. [27 [0] 4 3 4 6 -3

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Q: Determine whether the following polynomials span P2. P1 =4 -x+3x2, p2 = 4 + x, p3 = 24 + 2x + 6x2,…

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Q: MaxZ = 3X, + X, + 2X; %3D Sto 12X, +3X, +6X, +3X, =9 8X, + X, - 4X; + 2X; = 10 3X; - X, =0 X, 20.j…

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Q: Let X = (!,2) and T3} U = (1,2-)inel,2,U+ jult. %3D n+1 show that X is not T - space

A: This is a problem of Topology.

Q: axis the 28. Find the volume generated by revoluing obout the area bounded by the cunved x': 46x-y).…

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Q: -3 2 -3 2 (a) Give the elementary matrix that converts 2 -2 2 to -7 4 -2 -3 -1, To enter a matrix…

A: We need to convert -3212-22-2-3-1 to -321-745-2-3-1 We have A=-3212-22-2-3-1

Q: 1-2 Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates…

A: To fid the coordinates similar to a given polar coordinate we can use following formula…