Integrate G(x,y,z)=z-x over the portion of the graph of z=x+3y² that lies above the triangle in the xy-plane having vertices (0,0,0), (2,1,0), and (0,1,0).

Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: The distance from (-3,-4,-7) to the xz-plane is (A) -4 (B) (C) -3 (D) 3 (E) 4.

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Q: Find the equation of the plane containing the points (1,1,−2),(1,2,1),(−1,2,−2)

A: The equation of plane containing the points 1,1,-2, 1,2,1, and -1,2,-2 is to be evaluated.

Q: na piece of paper, sketch this square. et up double integrals to compute the area of this region in…

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: Determine the point on the graph of z = x² + y²+ 10 closer to the plane x + 2y-z = 0

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Q: Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes…

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

Q: Why does the graph of x2 + y2=4x has it's center at point (2,0)? and not (0,0). And how to try to…

A: Here equation we have given is of a circle : x2+y2=4x.

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2)…

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Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…