y z Show that the volume of the segment cut by the paraboloid+ 2,2 by the plane z=h equals half the segment's base times its altitude.

Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 45-5y² and the plane x +y…

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Q: Find the volume of the solid bound between the paraboloid z = x^2 + y^2 and the plane x + z = 0 as…

A: Given data: The given equation of paraboloid is z=x2+y2. The equation of the plane is x+z=0. (a)…

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: Find the volume of the solid cut from the cylinder x² + y? = 49 by the planes z = 0 and x + z = 1.

A: Image is attached with detailed solution.

Q: Which three dimensional figures when sliced by a plane cannot have a cross section that is a square?

A: When a rectangular pyramid is sliced by a plane then the obtained section will not be square.

Q: Determine the volume of the solid formed when a circle that passes through the points (l , 3), (3 ,…

A: As per the question we are given a circle passing through the three points : (1, 3) ; (3, 1) ; (1,…

Q: 2. Evaluate fff 2xdV, where G is the solid enclosed by the planes x + y + z = 1 and z = 0 and the…

A: Use the tripple integration format:

Q: Calculate the coordinate ỹ and z of centroid for a U-shape drainage enclosed by surface z = y²,…

A: According to the given information, it is required to determine the coordinate of centroid for U…

Q: Q3/ The surfaces p = 3, p=5, p = 100, p = 130, z= 3, and z= 4.5 define a closed surface. Find (a)…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: A certain parabolic monument has a base that is a parabola ( y=−.5x2+8y=−.5x2+8 ) And a front…

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Q: What quadric surface is the following an equation for and how do you know? -9x^2-3x+y^2+z^2= 1/4

A: The given quadratic equation is .We know that the quadratic surface of the form  form a cone.

Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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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: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: Find the exact volume of the solid formed in the first octant bounded above by the cone z = 2-√√x² +…

A: We have to find the exact volume of the solid formed in the first octant bounded above by the cone…

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: Solve the initial value problem dy - y = 2e' + 8e5t dt with y(0) 10.

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Q: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

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