Find the length of the curve r(t) = < 5 cos(t), 5 sin(t), 3t> for 0 ≤ t ≤ 2π Enter the exact value.

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Q: Question 6 Find the area of a triangle PQR, where P = (-3, 5, 1), Q = (-2,-5, 3), and R=(2, 3, 5)

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Q: 20. Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius…

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Q: Sketch the region enclosed by y = e5x, y = ex, and x = 1. Find the area of the region.

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A: topic;- application of integration

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Q: Determine the quadratic equation that has zeroes at -4 and 11, if f(-3)=56. Show all your work.

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Q: et f(x) [8− x − x² if x ≤ 2 12x - 5 if x > 2 Calculate the following limits. Enter "DNE" if the…

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Q: Determine the length of the parametric curve given x = 6 sint, y = 6 cost, ㅠ 0 ≤ t ≤=.

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Q: - Evaluate: [(5x¹ - 2x³ + 3x − 4)dx

A: We can solve the integration as below.

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A: To determine the length of the parametric curve given by x=sin3 t, y=cos3 t, 0≤t≤π2.

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Q: 3. Evaluate the following multiple integrals +¹(1+8x)dydx a. b. 0 x T xcos(xy)dydx

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Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

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Q: 11) Find the first derivative of y = (lnx) 4

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