(a) The moment of inertia of a surface about Sls x? + y? dS. Find the moment of inertia cylinder x? + y? = 3.

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y = 2r² (0 <t s…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Consider the surface S parametrized by R(u, v) (uv, sin u, cos v). Find an equation for the tangent…

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Q: 32. At what points does the helix r(t) = (sin t, cos t, t) intersect the sphere x? + y² + z² = 5?

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Q: Find the area of the surface of revolution generated by revolving the curve y = 5/ 0Sa<4, about the…

A: Given that:  y=5x,                        0≤x≤4

Q: Find the arc length of the parametric curve: x (t) = 1+ 3t2, y (t) = 4+ 2t³ ,0 <t < 6. Give your…

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Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point x = u?,…

A: x=u2 y=vu2 z=uv u=3 v=4 x1 =u2   x1 =9 y1 =vu2   y1=36 z1=uv z1 =12 we have to find the tangent…

Q: How many points are there on the surface 2 dx+y such that the tangent plane to the surface is…

A: We have given the a=6,b=9,c=9 d=max(a,b,c)=max(6,9,9)=9 The given surface is f(x,y,z)=9x2+y2-z We…

Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

Q: The parametric curve below x=2t3, y=(4/2)t2, Integral to find its length from (0,0) to (16,8)…

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Q: please be super detailed in the explanation!! For the shaded area shown in the figure, determine the…

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Q: Find the area of the surface generated by revolving the curve x = a cos θ,       y = b sin θ, 0 ≤ θ…

A: The curves x=acosθ,y=asinθ, and 0≤θ≤2π, we have to find the area of the surface generated by…

Q: Find the moment of inertia of a solid sphere of radius a about a diameter. (Take d = 1.)

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Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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Q: Q5/ Find the moment of inertia about the x-axis of a thin plate of density 8 = 1 bounded by the…

A: Given: Density δ = 1Circle x2+y2 = 4

Q: na on y =a sec 4 7. Find the radius of curvature at x =

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Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

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Q: x = tsin (4t), y = tcos (4t), 0 ≤ t ≤ π / 2, which is the surface area integral of the body formed…

A: The volume of the body by revolving around the x-axis in the parametric form is given as So only B,…

Q: Find an arc length parametrization of the line y = 8x. r:(s) = %3D

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Q: 36. Find the area of the surface generated by revolving the para- metric curve x = cos² 1, y = sin?…

A: Definition used -                               Area of the surface generated by revolving the…

Q: Determine the moment of inertia of the shaded area about the x-axis. 2" 10" y Answer: Ix Parabolic =…

A: To determine the moment of inertia about the x axis.

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =t, y = 21² (0 <…

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Q: Q2. A particle moving along the curve R(t)=(cost +1 sint)i + (sint -t cost)j,find acceleration…

A: Solution:

Q: Find the surface area of the solid gained by revolving the curve 0 < x < 14, about the x – axis. 14'

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Q: Describe the motion of a particle with posi- tion P(x, y) when x = 5 sin t, Y = 2 cost

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Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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Q: A thin plate of constant density d = 1 occupies the region enclosed by the curve y = 36/(2x + 3) and…

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Q: Q 6/ Compute the moment of * the Inertia for the shaded area with respect to the Y- — axis? 2 ft --…

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Q: The area of the surface obtained by rotating the curve y = V4-x², -2 s xs 2 about the x-axis is

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Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find the arclength of r(1) - (cost Ar sin r)i+ (sint-t cost)j+3k for %3D

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Q: The lateral surface area S of a right circularcone is related to the base radius r and height h by…

A: Since, the lateral surface area S of a right circular cone is related to the base radius 'r' and…

Q: denote the square of the arc length differential over the surface of Z=xy. What do you need to do to…

A: The differential path length is: ds=dx2+dy2+dz2    =dx2+dy2+dxy2    =dx2+dy2+xdy+ydx2

Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: 3) Find the radius of curvature for the parametric curve x = e-t cost , y = e-t sin t.

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Q: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x = t, y = 21² (0 < 1…

A: Given: x=t y=2t20≤t≤1

Q: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y= 21² (0 <…

A: Given: The curves,  x =t,  y = 2t2,   0 ≤ t ≤ 1 To find: The area of the surface generated by…

Q: *Q. ( 12 ), p. 410 : Find the area of the surface generated by revolving eУ + е-У the curve x = 0…

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Q: "ind the area of the surface generated by revolving the curve x = 2/1- y, –1< y <0 bout the y-axis.

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Q: Find the surface area of the solid of revolution obtained by rotating the the curve about the…

A: start with:

Q: Find the moment of inertia about the x-axis of a thin plate with density 8=1 bounded by the circle…

A: Given: The density of the plate =1 The plate is bounded by the circle =x2+y2=16

Q: Find the length of the curve #(t) = et cos(t), y = e* sin(t) for 0 <t < 5. %3D %3D Give an exact…

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Q: The 35-kg boy is sliding down the smooth spiral slide such that his z coordinate decreases 2 m per…

A: Solution is in step 2