Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo ,Yo ,Zo ) Show that the sum of the squares of the intersecting axes of the plane is constant.

Q: The equation of the tangent plane to the surface x² 8 at the point (-2, 1, 3) is Select one: 1/2…

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Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Find the area of the surface 2x^(3/2) + 2y^(3/2) - 3z = 0 above the square R: 0<= x<= 1,…

A: find z.

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: Can point normal form of a plane have no y? Leaving only constant (x - constant) + constant (z -…

A: Introduction: A aircraft is a flat, two-dimensional floor that extends to infinity in mathematics.…

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

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Q: Find equation of line normal to plane 3x + 2y- z = 5 and pass through Drigin point.

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Q: Find a vector equation of the normal line (the line orthogonal to the surface) for the surface…

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Q: The surface area of the surface generated by revolving y=x^3 , 0<=x<=1 about the x-axis is

A: We have to find the surface area of the region generated by y=x^3, 0&lt;=x&lt;=1 about the x-axis. I…

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 16 – x – y.…

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Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: A cylindrical surface in an xyz-coordinate system is an equation that contains only two of the…

A: In this question we have to state whether the given statement is true or false.

Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: An equation of the tangent plane to the surface y = 3 x-z at the point (-2,8, 2) is: %3D (A) 12…

A: y = 3x2 -z2 at the point (-2,8,2)f(x,y,z) = 3x2 - z2 -y∂f∂x = 6x, ∂f∂y = -1, ∂f∂z = -2zat point…

Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

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Q: Find parametric equations for the normal line to the surface x² + 9xyz + y² = 11z² at the point (1,…

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Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

A: Given Surface is xz + 2xy + yz = 10

Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

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Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

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Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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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: 9ху. Use hyperbolic functions to parametrize the intersection of the surfaces x - y = 49 and z =

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

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Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

Q: A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half…

A: Draw the region R as follows.

Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, -2, 2) is: (A) (x –…

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Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: Find the distance from the point (1, 1, 1) to the plane 2x + 2y + z = 0.

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: Solid created from these conditiong limited to 0eyet fiest actant on ly Positive xy-plane

A: y=xx=y2,0≤y≤10≤x≤y2z=1-yy=1-z0≤y≤1-z,0≤z≤1V=∫01∫01-z∫0y2 dx dy dz

Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

Q: Find an equation for the tangent plane to the surface z + 4 = ry* cos(z) at the point (4, 1, 0)

A: Solution: The objective is to find an equation for the tangent plane to the given surface

Q: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…

A: This is parameterisation of curve problem

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: the tangent plane of the surface [ x^2+y^2+z^2=14] at the point (1,3,2) O 3 x-6y + 4z = 28 2x+6y-4z…

A: Given problem:- the tangent plane of the surface [ x2 +y2+z2=14] at the point (1,3,2)

Q: Stress quadric surface of Cauchy g1ven by 6,2 18pr ulge O

A: No, the given is not the stress quadric surface of Cauchy.

Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…

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Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…

A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…