Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the solid enclosed by the hemi-sphere z = √(9 - x^2 + y^2) and the xy-plane

Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: A variable plane pes through a fixed point (a, b, c) and meets the uses at A, B and C. Show that the…

A: Given that a variable plane passes through a fixed point (a, b, c) and meets the uses at A, B, and…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+2y-z = 3. 0=0

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Q: Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3

A: This question is about application of derivative

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: Find the point on the sphere x^2 +y^2 +z^2 =4 which is closer to the point (1,-1,1)

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Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Consider the curve r(t) = (a) Pick any three points along the curve. Then find an equation of the…

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Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: True or False (iv) The line joining the Sun to a planet sweeps out equal areas in equal times. (v)…

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Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

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Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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