effF.d5 where F-dS Calculate F = (4x³z, 4y³z, 32¹) and S is the surface of the solid bounded by the hemispheres z = √16-2²-y², z = √1-x²-y² and the plane z = 0.

Q: What does 2x + y = 4 represent in the xy plane and what in the space?

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

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

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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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: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

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: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

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Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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