Find the points on the surface x^2+z^2-25=0, closest to the origin.

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: determine the type of the quadric surface  (x/3)2−(y/4)2− 2z2 = 0

A: given  (x/3)2−(y/4)2− 2z2 = 0 we need to find the type of quadric equation

Q: sketch the section of the surface

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: 22. z = 8 – x² – y?

A: To determine the sketch of the function.

Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 5z – 2z and…

A:

Q: Describe and sketch the surface 4x2 + y2 = 4

A:

Q: A frustum of a cone is generated by revolving the graph of y = 2x on the interval [2, 8] about the…

A: GIVEN FRUSTUM cone generated by revolving  the graph of y=2x on interval [2,8] about x axis  we need…

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. Label at…

A: y2=16+x2+z2

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x and the…

A: Answer

Q: There is a line through the origin that divides the region bounded by the parabola y = 8z – 32 and…

A: According to question given :There is a line through the origin that divides the region bounded By…

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

A:

Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 3? and…

A: The equation of the line passing through the origin is y=mx where m is the slope of the line. The…

Q: What is a trace of a surface?

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: The given equation of the parabola is,

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Find the area of the surface generated by revolving the curve y = / 2x - x , 0.75<x<1.75, about the…

A:

Q: Use disk method and draw a graph. √(9-y^2 ),y=1,y=3,x=0 about the y-axis

A:

Q: the solid cut from the first octant by the surface z = 81-x2-y

A:

Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

A:

Q: How many square units is the area of the region bounded by the parabolas y = x^2 and y = -x^2 + 4x ?

A:

Q: Sketch the surface x = 2y2 +3z2

A:

Q: Find the surface area of the portion of the half ball with radius which cuts off by the cylinder x2…

A: Concept: The surface area of the half ball is given by: A=∬1+∂z∂y2+∂z∂x2dA Where ∂z∂y, ∂z∂x is the…

Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

A:

Q: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotating it out of the xy-plane and around…

Q: 3. Explain how we know that it is possible to cut a surface with continuous boundaries in exactly…

A: We should mathematically establish the possibility of cutting a surface with continuous boundaries…

Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: There is a line through the origin that divides the region bounded by the parabola y 2x 5x? and the…

A: Shown below

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  y = Square root…

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Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

A:

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

A:

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

A:

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

A:

Q: Describe the appearance of a smooth surface with a local maximum at a point.

A: Solution:-  Describe the appearance of a smooth surface with a local maximum at a point.

Q: Find the exact area of the surface obtained by rotating the curve about the y-axis: y = 3 + 5x2 ; 3…

A:

Q: A frustum of a cone is generated by revolving the graph of y = 4x on the interval 32, 64 about the…

A: The surface area A=∫ab2π f(x) 1+f'(x)2dx

Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Find the exact surface area for the portion of the surface z=sqrt(x^2 + y^2) that is below z=4 and…

A: Find the exact surface area of the portion of the surfacez=x2+y2 that is below z=4 and in the region…

Q: 5. y-z =16

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine the maximum area of a rectangle inscribed in the ellipse x^2/49+y^2/81=1.

A:

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.