5. [6.1] If vector ā reaches from the origin to point (5, –7), determine the magnitude of ā.

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A: A multiple choice test that has 10 questions. Each question has 7 answer choices with one correct…

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A: To find the given line integral.

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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

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Given: I=∫sec5xtan3xdx   As we know that; The trigonometric identity; sec2x=tan2x+1 The Power rule;…

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A: Area

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A: We will solve the integration,

Q: Fred the fick partiel dervatives of he Amikinan = Oce /2 ニ for fy f2

A: Explanation of the answer is as follows

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A: If force field is conservative then it is independent of path.

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A:

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A: Given

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A: Given ,  The car you are interested in has 16 color options , 3 engine choices , and 6 entertainment…

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Q: 16. r=8sin ㅇ

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A: Apply greens theorem

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Q: 5. For each integral, state u, du, dv and v you would use to Integrate by parts a) fln(1+x) dx…

A: These integrals are solved integration by parts.

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A: Solution is given below:

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A: A detailed solution is given below

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A: According to the company rule we can answer only first question and rest can be reposted.

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Q: Va - 2 find: Va + 2 If f(x) = f'(x) = f'(2) = %3D Submit Question

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A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…