The value of . (x² +y²) dS, where S is the surface of the paraboloid z = 2- (x² + y2 ) above the x-y plane is equal to: 13T 111T 10 14 149 30 End Seme

Q: Hiwi Find the distance from the peint (er)tathe -Plane -4X-+4+ 2=4.

A: Recall:  The distance between the point (x0,y0,z0) to the plane ax+by+cz+d=0 is…

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

A:

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

A:

Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

Q: Find the surface area of that portion of the sphere x² + y² +2²= 8 which lies in the first octant,…

A: The given problem is to find the surface area of portion of the given surfaces. Given portion of…

Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

A:

Q: Find the point at which the line r(t) = (7, −7, 4) + t(−6, 6, −8) intersects the az plane.…

A: To find the point where the line intersects xz plane

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: hat is the scalar equation of the xy plane?

A: Given query is to find the scalar equation of the XY plane.

Q: V=R Prooflthat Nisavectors sPoe

A: Given that V = ℝ+ Operations + and · defined as, x + y = xy rx = xr, where x,y ∈V; r ∈F To prove: V…

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.