Find a generating curve and the axis of revolution for the surface                             x2 + 3y2 + z2 = 9.

Q: Describe and sketch the surface (x2/16) - (y2/9) + z2 = -1

A: The given surface x216-y29+z2=-1. We have to sketch the graph of the surface.

Q: Consider the Folowing equation of a quadric surface 4×^2+9y^2+9z^2=36 a. Find the intercepts with…

A: Given question is Consider the following equation of a quadratic surface4×^2+9y^2+9z^2=36. We have…

Q: Find the distance from the point (−1, −2, −3) to the plane 4x - 4y + 4z = 3.

A:

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Reduce each of the quadratic equations to its standard form and determine the name that classifies…

A: The quadratic equation is :The aim is to reduce the quadratic equation to its standard form…

Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: 9) Sketch the graph of the equation y² +2²=1 and correctly identify the surface.

A: Given: The equation is y2-x24+z2=1. To sketch: The graph of the given equation. To identify the…

Q: Identify and sketch the surface 9x² + y² − 2z² — 18x - 4y - 12z - 9 = 0. - Explain the position and…

A: The given surface is: 9x2+y2-2z2-18x-4y-12z-9=0. The given equation can be written as:…

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

A:

Q: (2x-y (22) + (x+2)- 3 = 1.

A: Given: Equation of the ellipse: Objective: To find the area of the interior of the ellipse.

Q: Put the quadric surface equation 4X (-8y + 4Z+39 = 0 into one of the standard forms, specify the…

A: The given quadric surface equation is           4x2+y2-z2-24x-8y+4z+39=0 Write the like terms…

Q: 6. Sketch the graphs of the following equations and identify the surface: (a) x² - 16y² = 4:² (b)…

A: (a) The equation x²- 16y²= 4z² is the equation of an hyperboloid of one sheet. To visualize the…

Q: Identify and sketch the surface r+y +- 2r +2 = 0.

A: Answer

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.