||r(t) × r"(t)|| Use the formula k(t) to find «(t). 3 r(t) = e%i+ ej %3D K(t)

Q: A torus formed by revolving the region bounded by the circle x2 + y2 = 49 about the line x = 8 (see…

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) : = 6ti –…

A: Solution is done in step 2

Q: find the equation for x in y=3x-x^3

A: Solving

Q: dx 2 X + 4

A: Topic = Integration

Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: ... 3x+ 2y + 4z = 12 12 15

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

A: Given; y=x^2 between x=1 to x=2

Q: Find the area of the region enclosed by the rose r = 18 cos 30. NOTE: Enter the exact answer. A = T

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: We have to find the volume by shell method.

Q: d Calculate ri(t) · r2(t)] and d dt [r1(t) x r2(t)] first by differentiating dt the product directly…

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Q: .

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Q: A property has been mapped, and the height above sea level is determined to be represented by the…

A: Given a scalar field representative of height.

Q: Find the center of mass of the given system of point masses lying on the x-axis. - 6, - 3, m,- 6 X1…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Given :r(t)=6costi+6sintj

Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: Find r'(t) %3D r'(t) = %3D

A: Given;  r(t)=6 sqrt(t)i +t2 sqrt(t)j +ln(t2)k.

Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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Q: Represent the plane curve by a vector-valued function

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

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Q: Find the directional derivative of the function at P in the direction of v f(x, y) = x³ - y³, P(6,…

A: we have to find directional derivative.

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = T, using 4 trapezoids.…

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Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

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

Q: f" (x) = cos x, f(0) = 1, f'(0) = 2, f'"(0) = 3.

A:

Q: y=2\4-x²

A: Since we are given with the multiple number of question and our guideline is solve first question…

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

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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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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Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x + x)dx. (5 points) 2.…

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Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

A:

Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: Find div F and curl F if F(x,y, z) = 4y®z³i – 7x°z*j – 3xy°k. div F=|0 curl F=

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Q: Use double integration to find the volume of the solid bounded by the paraboloid 2 = 9X- + y, below…

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Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The point P(8, - 10) is on the terminal side of an angle e in standard position. What is sec(e)?

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Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

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Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

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Q: (b) trte) × u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

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