Answered: Tangent of x2/3 + y2/3 + z2/3 = a²/3…

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

See similar textbooks

Related questions

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

A: find z.

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

A: Given surface is 9x2+4y2=30 and plane is 9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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…

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

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

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<=x<=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…

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

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

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

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).

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

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

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…

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

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,…

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

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

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

Q: the trace of the surface in the plane x=1?

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 )

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…

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

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.

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

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: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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…

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 :-…

Question

could you please figure it out step by step?

Tangent of x?/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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Perimeter$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

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.
Can point normal form of a plane have no y? Leaving only constant (x - constant) + constant (z - constant) = 0?
IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square 0<= x <= 1, 0<=y<=1, in the xy-plane
Discuss Green’s Theorem in the Plane?
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.)
Parameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.
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: ____________
A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and two fixed points (called _____) is a positive constant.
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 you
How do you integrate a scalar function over a parametrized surface? Of surfaces that are defined implicitly or in explicit form? Give examples.
Find the distance from the point (1,1,1) to the plane 2x+2y+z=0
The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.