Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9 and the coordinate planes.

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a…

A: To determine the surface area of the frustum.

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

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Q: Find the point(s) on the surface z2 = xy+1 which are closest to the point (10, 8, 0). List points as…

A: The objective is to find the points on the surface z2=xy+1 which are the closest to the point 10,8,0…

Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

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: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: 1 in 1in y 1 in 3 in 1 in X

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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: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

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

A: Please check the next step for details

Q: Please write the solution in paper

A: Since the question has multiple sub parts we will solve the first part only. Please resend the…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Find the centroid of the triangle bounded by y = x, y = 14-x, and y = 0. Draw the graph.

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Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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