Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your answer correct to 4 decimal places. Answer:

Q: Determine the volume generated when the area bounded by the curves y = sin x and y = cos x from x =…

A: Given problem:- Determine the volume generated when the area bounded by the curves y = sin x and y =…

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Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

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Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

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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: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

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A: Use the washer method to find the volume of rotation of the solid.

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = Xx. A 1 в) 4 0.5 D 3

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Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: dx dy =

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Q: Question 16 Use a triple integral to find the volume of the solid. The solid bounded by the surface…

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Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

A: Given problem:-

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Question 8 Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the…

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Q: Evaluate the iterated integral. 4ze dy dx dz

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Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: Describe the graph of the equation. r = (5 – 31) i – 81 j O It is a line in 2-space that goes…

A: Given : r=(5-3t)i-8tj

Q: (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D…

A: As you mentioned part b is solved

Q: Question 14 1. 2 Evaluate the iterated integral. J, J. J. (x²+ y² + z?) dx dy dz -1°0 (А) 5 (в) з D)…

A: To find following integral valueI=∫-11∫02∫01(x2+y2+z2)dx.dy.dz

Q: Evaluate (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) Need…

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t?k, u(t) = 4ti + t²j…

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Q: Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

A: We need to evaluate integral.

Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

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Q: Let f(x) = 9x* + xx² + e2*. Compute f©(x). (Use symbolic notation and fractions where needed.) f9(x)…

A: Compute 5th derivative of f(x)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

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Q: Find T(t) and N(t) at the given point. = e' cos t, y = e' sin t, z = e'; t= 0

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Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

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Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

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Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

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Q: Consider the vectors: a = -11î + 10j +–12k, b = 2î + -8j + -12K, c = -7î +-10j + 10k a) Find: bxc =…

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