Find the isogonal trojecdories of x*+y² =r² at 45",

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

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Q: 5- 4- Find the volume of the solid created by rotating the following curve y = 3vx about the y-axis.…

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: 2. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: The arc y=2 sqrt root(x) from x ∈ [4,16] is rotated about the x axis. Find the exact surface area…

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Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: What is the area of the conic (x + 3) + y 25

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Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by…

Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

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Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: vo ume of the solid in the litoctanit bounded by the plan 2x+3u +62=12

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Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about x-axis.

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: Find the centroid of the region bounded by the given curves. y = 8 sin(5x), у 38 cos(5x), х-D0, х 3…

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Q: Give an example of a plate such that its center of mass does not occur at any point on the plate.

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Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: 4. у%3D 2х—х2, y = 2x² – 4x

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Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 40,0 ≤ 0 ≤…

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

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Q: A thin plate has mass 3. What is the x-moment of the plate if its center of mass has coordinates (2,…

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Q: Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between…

A: Apply the divergence theorem for the hollow region which is bounded by 2 surfaces. Consider D as the…

Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: A point moves along the intersection of the elliptic paraboloid z = 4x + 11y and the plane y = 4. At…

A: given information is z=4x2+11y2 The plane y=4To find :Rate of change of z with respect to x when the…

Q: The area of the rotational surface resulting from rotating x² + y2 = a² about the x axis is? the arc…

A: Given : x2 + y2 = a2

Q: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

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Q: Find the average z-coordinate of points in a hemisphere of radius 8 centered at the origin with its…

A: We have to find the average z coordinate of the hemisphere of radius 8 centered at origin with base…

Q: Find the area of the surface obtained by rotating y = cosh x over [−ln 2, ln 2] around the x-axis.

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Q: Sketch the region enclosed by the given curves. y = 7 cos(2x), y 7-7 cos(2x), 0 sxs x/2

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Q: Find the solid of revolution that results when the region under the graph of f(x) = xvsin x for 0< x…

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Q: Find the area of the surface generated by revolving the curve y = Osxs2, about the x-axis. 9

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Q: The arc y=2 sqrt(x) from x∈[4,16] is rotated about the x axis. Find the exact surface area…

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Q: Sketch the region enclosed by the given curves. y = 4 cos(5x), y = 4 – 4 cos(5x), 0sxS a/5

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Q: *Sketch all appropriate regions or solids." Evaluate the integral [[2y² cos(xy) dydx.

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Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2