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: The surface of a paraboloid results from rotating a parabola about it's axis. The parametric form is…

A: 1 )Equation of a Parabola:The standard equation of a parabola in the xy-plane is given by  where a…

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: 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 the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

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: 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: How do you integrate a scalar function over a parametrized surface? Of surfaces that are defined…

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Q: Use the polar coordinates to find the surface area of the part of the conical surface z^2 = x^2 +…

A: Given conical surface is z2=x2+y2 that lies above the semi-circle y=2-x2

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: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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