Find the coordinates of the centroid of the curve given belov x = cos t+tsin t, y =t cos t- sin t, 0sts, 2

Q: find the length of the indicated portion of the curve. 11. r(t) = (4 cos t)i + (4 sin t)j + 3t k,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose F(x, y) = -yi + xj and C is the line segment from point P = Q = (0,4). (5,0) to (a) Find a…

A: The solution are next step

Q: Find the line integral with respect to arc length (8x + 9y)ds, where C is the line segment in the…

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Q: Determine the centroid of the lamina bounded by y=sin x, y= cos x and x= 0 in the interval 0,

A: Plot the curve and find the area of the area enclosed by the curves. The shaded region is the area…

Q: This is a three part problem. Given: Find the line integral with respect to arc length (6x + 8y)ds,…

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Q: can u help me with this Jacobian question please

A: Given transformation is

Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

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Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: Find the coordinates of the centroid of the curve x = e^t cos t, y = e^t sin t, 0<=t<= pai.

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Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0<=t <= pai.

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Q: Find the equation of the tangent plane to the surface z = ln (2x + y) at the point (-1,3,0) .…

A: To find the equation of the tangent plane to the surface z=ln2x+y at the point -1, 3, 0.

Q: 14. (a) Give a parametrization for the intersection of y = x² and z = e". (b) Set up an integral…

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Q: Suppose F(x, y) = -yi + xj and C is the line segment from point P = (5,0) to Q = (0, 3). (a) Find a…

A: Given: F→(x, y)=-yi→+xj→For part(d)we know∫TF→.dr→=∫C1F→.dr→+∫C2F→.dr→+∫C3F→.dr→where T is the…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. x? from the origin to the (a) Find a vector parametric…

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Q: Find the centroid of the region enclosed by the x-axis and the cycloid arch x = a(t - sin t), y =…

A: Given data:

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

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Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

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Q: 5. Consider the saddle surface r = y- 2, find the point where the tangent plane is parallel to x+y+z…

A: If two vectors a1, b1, c1 and a2, b2, c2 are parallel, then it can be written that a1, b1, c1=ka2,…

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0 … t ……

A: coordinates of the centroid of the curve  x=cost+tsinty=sint-tcost…

Q: Suppose F(x, y) = (2y, – sin(y)) and C is the circle of radius 7 centered at the origin oriented…

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Q: Find the line integral with respect to arc length / Q = (0,3). (2x + 7y)ds, where C is the line…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. Find a vector parametric equation for the parabola y = x²…

A: The solution is following.

Q: Let C be the (oriented) curve in the plane given by the graph of y = x² from the point (0,0) to the…

A: C  be the curve y=x2  from 0,0  to 2,4a  fx,y=2x

Q: Find the line integral with respect to arc length|| (9x + 8y)ds, where C is the line segment in the…

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Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

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Q: Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2,…

A: To determine the first order (linear ) approximation to f(x,y) at the given point

Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: 4. Integrate f(x, y, z) = Vx² + y² over the involute curve (cos t + t sin t)i + (sin t – t cos t)j,…

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve = (2x –…

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Q: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: Suppose F(x, y) = x²i + yj and C is the line segment segment from point P = (2, –1) to Q = (4, –4).…

A: We need to evaluate integral.

Q: Suppose F(x, y) = (2y, – sin(y)) and C is the circle of radius 8 centered at the origin oriented…

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Q: Suppose F(x, y) = -yi + xj and C is the line segment from point P (3,0) to Q = (0, 2). (a) Find a…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve+ 1 from…

A: Given: f(x,y)=2xy From the point (3,0) hesta (0,2)

Q: E For the surface f(x,y, z) = tan(xy + %3D at (0,1,0) in the direction of ü = i- 2j +2k; (3) the…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

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Q: Find the coordinates of the centroid of the curvex = cos t + t sin t, y = sin t - t cos t, 0 ≤ t≤…

A: Given, the curve x = cost + t sint, y = sint – t cost, [0,pi/2].

Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

A: Given F→(x,y) = -ysin(x)i→+cos(x)j→ a) Let us assume x=t then y=x2=t2 by differentiating r→(t) with…

Q: Find the coordinates of the centroid of the curvex = cos t, y = t + sin t, 0 ≤ t ≤ p.

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Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: please answer the (a) (b) (c)  parts

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Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Q: Find the divergence and curl of F = (e¬* sin y , e¯Y sin z , e-² sin x). %3D

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Q: Find the line integral with respect to arc length (2x + 6y)ds, where C is the line segment in the…

A: The solution of line integral is given as follows :