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Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: Use Green's Theorem to find the work done by the force field F(x, y) Vyi + Væj on a particle that…

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Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

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Q: Ben is a fisherman with a boat in Rhyl harbour. This is part of a graph of the depth of water at the…

A: According to guidelines,  we must answer only three of the multipart questions given. Please…

Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: An isotope of the element erbium has a half-life of approximately 9 hours. Initially there are 7…

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Q: Verify the formula F.n dS div FdV in the Divergence Theorem by evaluating the surface integral and…

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Q: 22. Find the function for a parabolic arch that has a base length of 24 feet and a height of 36…

A: Equation of parabolic curve is given and in form X^2 = 4aY

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i +3 sin(t)j +…

A: Solution is given below:

Q: An investment grew by 4% in the first year, 6% in the second year and 10% in the third year with…

A: Annual average growth rate is calculated as sum of each year growth rate divided by the number of…

Q: A business determines P(40) = 3000, %3D P'(x)0 where P(x) is the profit in thousands of dollars at a…

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Q: Evaluate (2x - y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 5

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Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: ,2 -1 dx 2

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Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: Solution is given below:

Q: 3. Suppose that the revenue in selling x tables is equal to 200x – 0.25x2 dollars, and producing a…

A: Suppose that the revenue in selling x tables is equal to 200x-0.25x2 dollars, and producing a table…

Q: 10. Consider the system of equations X, - 2x, + 3x, = 1 2х, — Зх, — 2х, 3 3 X, - x, - 5x, = 2 a.…

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Q: 3 5) Differentiate with respect to x: y = %3D 3x e

A: Solving the problem by finding the differentiation.

Q: Q1. Which of these expressions is NOT factorised? А. X(х + 1)(х + 2) В. (х+ 1)(х+2) С. x (х + у) —…

A: Solving the problem by finding the correct answer.

Q: what is 2x2

A: 2×2= 4

Q: Write the equation of a sine or cosine function to describe the graph.

A: We know the general form of sine isy=asin(k(x-θ))+bb is the vertical shift of the graphfrom graph…

Q: - If g(x) 1 dt , find g'(2). 4 +t

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0<t< 2n L= 75.66

A: arc length

Q: Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.

A: Given, x²-y+1=0 I.e, x= sqrt(y-1)----- equation 1 x-y+1=0 I.e, x= y-1 ----equation 2

Q: [6x? arcsin(x)]dx

A:

Q: b. Shown below is the graph of a function f(x). Determine the value of each of the following. i.…

A: Topic:- application of integration

Q: Consider the plane curve given by the parametric equations x = t + 22t – 23 y = t2 + 22t – 5 -- What…

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Q: 2 у2 | dxdy 1 у 2.

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Q: 16 Find the constants a, b, c, d, e for the ellipse r = 6+2cos0

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Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

Q: For the linear transformation T: R* - R, T(v) = Av, find T(1, 0, 2, 3) and the preimage of (0, 0,…

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Q: The function f is given by f(x)=9.x^2/3+3x-6 has a relative minimum at x=? A. -8 B.-1 C.-1/8 D.0

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Find your answer below

Q: Let f(x) = x^2 . Describe a series of transformations which could map f(x) onto g(x). Then write an…

A: Here we have to do the transformations to the graph of f(x) so that it mapped on to g(x).

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x2 - c and y = c – x² is…

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Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: T between -1 and 1, then find a number c in [-1,1] where Find the average value fave of f(r) f(c) =…

A: This question can be solved using the concept of average value of a function in a given interval.

Q: Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: To calculate ddtr1t·r2t and ddtr1t×r2t first by differentiating the product directly and then by…

Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

A:

Q: Let fx) = mx + b where m and b are constants. If lim fx) = 1 and lim Ax) = -1, determine m and b.

A: Given: fx=mx+b And limx→2fx=1 and limx→3fx=-1

Q: determine the interval and radius of convergence 1 Z-3)2+"(n² + 1) (4x - 12)" n=0

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i+ (y – x)j+ (z – y)k - across…

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Q: 10 – Vx dx V2x2

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Q: Use Green's theorem to calculate.(2x³ – y*)dx + (x³ +y*)dy, where C is the boundary of the annular…

A: Apply greens theorem

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where U + dy

A: Given

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find a power series solution around xo = 0 for y" – xy = 0

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