Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) + s(4,-5,1). Please answer  Thank you.

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A: This question is based on finding equation of tangent plane.

Q: Use polar coordinates to evaluate the double integral. 19y dA, where R is bounded by r-2-cos(0)

A: To use polar coordinates  that are: x=r cos θ, y=r sin θ & dA=r dr dθ 0≤r≤2-cos θ0≤θ≤2π

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Q: The following refer to the following data set: 87 40 67 80 32 87 28 96 27 88 84 What is the mean (2)…

A: The given data set is: 87 40 67 80 32 87 28 96 27 88 84 The mean is the average value in a…

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Q: Σ (-1)"x2n (2n)! 1. For all x E R, cos x = n=0 (a) Find a power series that is equal to a cos(x²)…

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Q: 9. A population of fish increases by 8 every minute. If there are initially 1600 fish, find a…

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Q: (-2t +1 if t<B if t 2B Given the function h(t) = %3D Determine one value for ß for which the…

A: Use the definition of continuous function.

Q: How do we estimate lim,- f (x) NUMERICALLY? O pick one value of x close to "a" to see what f(a) is…

A: Find your answer below

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Q: Given two functions h(t) and g(t), is h¯1g-1 (t) = (hg)-1(t).

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Q: Find f. f '(t) = 4/(1+t^2)     f(1) = 0

A: Topic = Integration

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A: Given

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Q: Consider the following. 6. 13 In(x) dx Let u = In(x). Find du. %3D du = dx Indicate how the limits…

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Q: 6. Simplify each of the following using the properties of logarithms: (a) In ) (b) log2(Vt5)

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Q: D03 Mathematics for Social Sciences I | S2 21/22 courses / ECON1003 | S2 21/22/ General / Graded…

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Q: How would you classify the sequence 0.45,0.045, 0.0045, 0.00045, ........... А. Arithmetic Series В.…

A: 0.45, 0.045, 0.0045, 0.00045,..........a1=0.45a2=0.045a3=0.0045a4=0.00045Ratios of two adjacent…

Q: Find f. f"(e) = sin(e) + cos(e), f(0) = 5, f(0) = 4

A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

A: Formula used:logan=nlogalogab=log(a)-log(b)loga.b=log(a)+log(b)

Q: Find term 4, term 6 and term 8 given by the formula: n2 +n+6 a n ;n2 1. n+7 Determine whether the…

A: an=n2+n+6n+7 For n=4a4=(4)2+4+64+7=2611For n=6a6=(6)2+6+66+7=4813For…

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Q: 1 19. x(x² + 1)

A: Solving the problem by finding the partial fraction decomposition.

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A: Given problem:-

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Q: A particle moves in a straight line and has acceleration given by a(t) = 12t + 5 sin t. Its initial…

A: To find the position of the function s(t) of the particle. Given that a(t)=12t+5sin(t) Initial…

Q: 4. Find the number of surjections from {1, 2,..., m} to {1, 2, ... , n} such that no element in the…

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