Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola y = 4 - x² and the line y = -3x, while the top of the solid is bounded by the plane z = x + 8.

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the surface area of the part of the sphere x² + y² + z² = 81 that lies above the cone z =…

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Q: Find the volume of the solid that lies under the plane 4x + 6y − 2z + 15 = 0 and above the rectangle…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 − x2 + 3 and above…

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Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

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Q: the surface z = &x + 4y th=

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

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 surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x²…

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Find the surface area of that part of the plane 8x + 6y + z = 5 that lies inside the elliptic…

A: Given that the equation of a plane                                         8x+6y+z=5. To find the…

Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

A: Let z=fx,y. Differentiate the function fx,y with respect to x and y, to obtain fxx,y and fyx,y.…

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: -3x+24+2=6 that lies ab 2 the Curves y=x² in the X-

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Q: Find the surface area of that part of the plane 2x + 3y + z = 3 that lies inside the elliptic…

A: Given: The plane is: 2x+3y+z=3. The elliptic cylinder is: x225+y29=1. To Find: The surface area of…

Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y² = 5x,…

A: The region in the first quadrant bounded by the given curves is plotted below. See that for the…

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3