Compute the line integral of the scalar function f(x, y) = /1+9xy over the curve y = x³ for 0 < x < 8 Se F(x, y) ds

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A: The union of two sets A and B means the set that contains all elements of A and B.

Q: 05 Fill in the Blank Text What is the surface area of the composite figure? 6 mm 15 mm 6 mm 9 mm 5…

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Q: 4. Solve the initial value problem: y(0) = 4, y'(0) = 3, where the function y(x) is a solution %3D…

A: Given differential equation is y'' + y = 0 with y(0) = 4, y'(0) = 3

Q: Let a, b and c be integers. (i) If cla and alb then cb. (iv) If cla and cļb then c(sa +tb) for all…

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Q: Find the solution. y'+=V5.y(1) = 0 x+ 3x 2 - 3 A) y = 9x 3 x³ – 2x 2 + 1 (B y = 9x 3 x-3+2x 2 y = 9x…

A: Given y' + yx = y with y(1) = 0

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Q: 7. (a) A computer is programmed to choose an integer between 1 and 99, inclusive, so that the…

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Q: 4. Let ao, ɑ1, a2, be the sequence defined recursively as follows. ... Ak = 2ak-1 – 3, for all…

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Q: The total budgeted cost of a project is 899,642 dollars. The project completion time is 21 weeks.…

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Q: Determine whether the events are mutually exclusive or not mutually exclusive then find the…

A: Here given the sample space is S=1, 2, 3, 4, ...,20 And two events A=even number between 1 to 20=2,…

Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: Step 2 () * - () • (::)() one must find : et et dt insort glan () ) in the at tt 7- e et dt gives: -…

A: Please check next step.- also consider giving precise question from now on.

Q: (a) The temperature in space given by T(x, y, z) = 200xyz^2. Find the hottest temperature on a unit…

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Q: Find the solution. y'-y =y?e* с —х A y = B y = с — х C) y = C+x с +x D y =

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Q: 1. Define function f : Z+ → Z such that f(n) = /n. (a) Is f one-to-one? Justify (prove) your answer.

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Q: Q2/Evaluate SR SV - 2x2)dA Where Ris the region bounded by |x| + lyl = 1?

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Q: Date: Afincduse Partial fractin -2X+4 2.

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Q: Consider the complex numbers: z = 2 – i and w = 1+3i . Sketch (in the same diagram) 2, w, zw and z:

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Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = P + 4e',…

A: Given differential equation is y'' + 4y = t2 + 4et with y(0) = 0, y'(0) = 9

Q: Mar ) Find all the dimensions of your solid (eg. length, width, height) in centimetres. Length =…

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Q: Find a vector equation with parameter t for the line of intersection of the planes a + y + z = 4 and…

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Q: 9. Find a basis y1(x), Y2(x) of the space of solutions to y" = Y such that Y1 (0) = 1, y (0) = 0,…

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Q: Question 20 of 25 13x Match the point in polar coordinates 2, 4 to the points A, B, C, or D.

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Q: 4. Find the particular solution of the DE: -2t y" + 4y' + 4y = te *

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Q: %3B 20 40 . 10. (a) y(0) = 8 20 20 20 10 10 0 10 -20 -10 10 20 -20 -10 10 20 -20 10 20 -20 -10 10 20…

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Q: Prove that (a, b) | = |(c, d) | for any numbers a, b, c, d where a <b and e<d. Proof:

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Q: Do the three planes x, +2x2 + x3 = 5, x2 - x3 = 1, and 3x, + 9x2 = 13 have at least one common point…

A: Given planes are  x1+2x2+x3=5x2−x3=13x1+9x2=13..........1 Write the above system in matrix form…

Q: For which of the following g(x) is r = v3 a fixed point? Use x, = 1. Stop your cakculation at the…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: (b) Let A(4, 4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

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Q: Exercise. A curve C is described by the vector-valued function p(t) = (t, 4 – 21,² +2). Exercise.…

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Q: A colony of bacteria starts with 2000 individuals. The colony is exposed to a new penicillin-type…

A: (a) The average rate of change of a function f over the interval  is given by fa-fbb-a. At t=20 and…

Q: (b) Find the curvature and the radius of curvature of the curve r (t) = e'i+ e-tj+ tk at t = 0.

A: b Given curve is rt→=eti^+e−tj^+tk^. We have to find the curvature of he curve rt→=eti^+e−tj^+tk^ at…

Q: Example 1.2.1 Here are two simple examples of set equality on the real line for you to verify. (i) U…

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Q: Why does the linear congruence 25x ≡ 30 (mod 75) have no solutions?

A: To show that the linear congruence 25x≡30mod 75 have no solutions.

Q: 10 Find the projection of v = -14 onto the | -15 -4 -4 3 subspace W of R' spanned by| -6 and 6. 1…

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Q: Prove that if a > 0, k > 1, and ak -1 is prime, then a = 2 and k is prime. %3D

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