Deternime the equation of the tangent plane to the surface givne by the equation G(u, v) = (u^2 – v^2, u + v, u – v) at the point where: u = 2, v = 3.
Q: = 21 which is parallel to the plane Find the equation of tangent plane to the surface x? + 2y? + 3z2…
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Q: Find the points on the surfacex - yz = 9 that are closest to the origin. Enter your answers in order…
A: The given surface is: x2-yz=9⇒x2-yz-9=0 ............(1) We have to find the points on the given…
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A: The equation of two planes are x-2y+z = 0 ...... (1) 2x+3y-2z = 0 ...... (2) Angle between…
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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z2 22, P = (2,…
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Q: Parametric equations for the curve of intersection of the cylinder 9x2 + y² = 9 and the plane x + y…
A: Let x=sint, substitute this into the equation of cylinder, so…
Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point (Xo , Yo , Zo ) Show that the sum of the…
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Q: Equation of the tangent plane to the surface 7(u,v) at (uo,Vo) is given by 7-7(uo, Vo)]× Ñ(uo,Vo)…
A: To find: Equation of the tangent plane to the surface r→u,v at u0,v0
Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…
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Q: Solve the problem. Find the equation for the tangent plane to the surface z=2x2+10y2 at the point…
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Find the equation of tangent plane and normal lines of the surface: t the point (1,3, 2).
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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…
A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…
Q: Find equations for all the planes that intersect the y-axis at y =1 and the z-axis at z =2, and are…
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Q: Ouestion #2- (@). Find the tangent plane and nor mal line of the Surface. y.2)=28ay²-62+5zo at poit…
A: Hello. Since your question has multiple parts, we will solve the first parts for you. If you want…
Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…
A: Planet is spherical;g(x,y,z) =x2+ y2+z2 = 144M(x,y,z) =12x - y2+xz + 210 We need to satisfy,∇ M =λ…
Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo ,Yo ,Zo ) Show that the sum of the…
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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…
A: Given: Mx,y,z=The strength of the magnetic fieldMx,y,z=12x-y2+xz+210…
Q: Find the points on the surface.x - yz = 4 that are closest to the origin. Enter your answers in…
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Q: Solve the problem. Find the equation for the tangent plane to the surface z=-3x2 - Sy2 at the point…
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Q: Solve the problem. Find the equation for the tangent plane to the surface x2 + 10xvz + y = -8z2 at…
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Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo , Yo , Zo ) Show that the sum of the…
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Q: usuƏp seu pin 100 kg/m and flowS With Ve Zk, whei y, and z are measurec in meters, and the…
A: Density of fluid=1100kg/m3 Flow with velocity v=xi^+yj^+kz^ To find the rate of flow outward through…
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: Use cylindrical coordinates to evaluate V9-x² r9-x²-y² a² dz dy dx -3 J- 9-x² Jo Do not forget to…
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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…
A: As per our guideline we are supposed to be answer only one question you can repost other questions…
Q: Find the area of the surface generated by revolving the curve y = / 2x - x , 0.75<x<1.75, about the…
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Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…
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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 the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…
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Q: etermine the equation of the plane tangent to the surface x2 + y² – z² = –1 at the point , 1, v3).
A: To find The equation of the plane tangent to the surface at the given point.
Q: 5. (10 points) Find an equation of the tangent plane to the surface given by z2 – 2x2 – 2y² = 12 at…
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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…
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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: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, –-2,2) is: %3D (A) (x…
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Q: Tangent of x²2/3 + y2/3 + z²/3 = a²/3 surface at any point (Xo , Yo ,Zo ) Show that the sum of the…
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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: Find the equation oftangent plane and normal lines of the surface: ƒ(x, y, z) = 10x² –14 y² +11z³-7…
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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: The two surfaces x2 + y2 + z? = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…
A: We have to find angle between two tangents - First we will find divergence of function f at point…
Q: Find a parameterization for a circle of radius 4 with center (-3,-1,2) in a plane parallel to the xz…
A: Aim: To find the parametric equation for the circle of radius with radius 4 and center -3, -1, 2…
Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…
A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0 ...............(1)where,x0,…
Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…
A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…
Q: Find a parametrization of the line in which the planes x + 2y - 2z = 1 and 3x + 3y – 3z = 0…
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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: Find the points on the surfacex - yz = 9 that are closest to the origin. Enter your answers in order…
A: Given: x2-yz=9 Using Lagrange multipliers, The distance from any point to the origin is:…
Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z? = 22, P =…
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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 point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…
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Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find the (linear) equation of the tangent plane to the surface z=xsin(x+y) at the point (7,−7,0). Your answer should be in the form of an equation, e.g., something like ax+by+cz=d or a(x−x0)+b(y−y0)+c(z−z0)=0 would work. Equation: ____________Find the (linear) equation of the tangent plane to the surface z=xexy at the point (7,0,7). Your answer should be in the form of an equation, e.g., something like ax+by+cz=d or a(x−x0)+b(y−y0)+c(z−z0)=0 would work. Equation:______________________
- Find a parametrization for the line perpendicular to (4,-1,1), parallel to the plane 4x+y-8z=1, and passing through the point (1,0,5). (Use parameter t. Enter your answer as a comma-separated list of equations.)A particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine the particle’s trajectory y(x) and sketch its graph. Determine the speed of the particle as a function of time. Find the angle ϕ between the velocity vector and the x−axis.Find the coordinates of the point (x, y, z) on the plane z = 3 x + 3 y + 3 which is closest to the origin. x=-----y=------z=-----
- Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x and y axes and the line y=-x+1? Thank youFind a parametrization of the curve. The vertical line passing through the point (3, 2, 0)Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane tangent to S, at the point (1, 0, 2), is given by:
- F(x,y,z)=2x2+7y2+7z2 F(x,y,z)= 1152 The unit vector u for which the directional derivative is maximum at point (11,7,9) is ? What is the maximum directional derivative at the point (11,7,9) ?find parametric equations for the line tangent tothe curve of intersection of the surfaces at the given point. urfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (√2, √2, 4)A baseball is hit from a height of 3.5 feet above the ground with an initial speed of a 110 feet per second and at the angle of 45ﾟ above the horizontal.( Assume the model of projectile motion with no air resistance and g=32 feet per second) (a) find the max height reached by the baseball (b)determin whether it will clear an 8 foot high fence located 375 feet from home plate