Find the volume of the solid that lies under the plane 4x + 6y – 2z + 17 = 0 and above the rectangle R = {(x, y) I -1 < xs 2, -1 sys 1}. 60

Q: A flat circular plate has the shape of the region x² + y² ≤ 1. The plate, including the boundary…

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Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: 2 x = 8 - y, x =y - 8

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Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: The centroid of the T-section shown is 2.5 inches above the base. What should be the value of b to…

A: Given information is as follows:The area of the shape is,The centroids are as

Q: f(x) = √√/x = -²x³12 about the x-axis for 1 ≤ x ≤ 3. .3/2

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Q: Find the surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the…

A: The object is obtained by rotating about the x-axis over the interval .We have to find the surface…

Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

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Q: Let R be the rectangular region with (1,2) , (2,3) , (3,2) and (2,1) as corners. Use change of…

A: Changing the variables

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.

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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: Find the centroid

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Q: 6. Find the area of the part of the surface z = x²-y², which lies in the first octant that is inside…

A: The solution is given by

Q: Find the surface area of the portion of the cylinder x² + z² =4 above the rectangle R = {(x,y) |…

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Q: 6. The figure shows the surface created when the cylinder y² +2²=1 intersects the cylinder ²+²=1.…

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: ). Explain how we get the Cylinder by equivalent relation.

A: Please check the next step for details

Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A 92/6 s.u. B 92/4 s.u.…

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