Write the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture:4x2-3y2=12, Ox

Q: The center of a ceiling fan is at (2, 8). If the radius is 12in, what equation represents the outer…

A:

Q: Calculate the equation of the circle that passes through the point (0, -3), whose radius is V5 and…

A: we know that equation of circle (x-h)2+(y-k)2=r2  Here radius of circle is 5 ,here circle passing…

Q: ecall the equation for a circle with center (h,k)(h,k) and radius r. At what point in the first…

A:

Q: ngent to the y axis and the center is

A: To determine the circle of equation tangent to y axis and center (5,8)

Q: Identify the surface with equation 9r? - 4y? + 16z? - 144 = 0. %3D

A: Given the equation : 9x2-4y2+16z2-144=0 We know Equation of hyperboloid of one sheet:…

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

A:

Q: name the surface represented by the equation r^2+z^2=4-2z

A:

Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

A:

Q: Describe in words the surface whose equation is given. p = 5

A:

Q: Identify the surface in Cartesian coordinate for each of the following equations. а) р-5 and b)…

A: The solution is given below.

Q: d. x-2x +y? + z = 3

A:

Q: Write the standard equation for the circle. center (10, -6), r = 6 O a 2 (x + 10) + (y - 6) = 6 O b…

A: The standard form of the circle with center (h,k) and radius r is given by: (x-h)2+(y-k)2=r2

Q: Find the parametric form of (i) the circle x?+y? =p²

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Sketch and identify the surface given by the equation Z=: x² +

A:

Q: x² + + =1 y2 9. 4

A:

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

Q: Sketch the given surface

A: Given: x42+y82+z122=1 The given equation is an ellipsoid.

Q: Find the distance between the centers of the two circles x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x…

A:

Q: cribe the surface with equation 2 +y +? + 8x + 6y + 2z - 10 = 0 surface is a sphere with center ( i…

A:

Q: Write the equation for the surface generated by the revolving curve y = 2x +1, revolved around the x…

A:

Q: Which of the following equations describes a circle on a coordinate plane with a radius of 8 units?…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the angle of intersection.of the curves X+yー4 dd xt=4メ 2. %D

A: The angle of intersection between 2 overlapping circles is the angle between the tangents at any of…

Q: Describe and sketch the surface in R3 represented by the equation x+y = 2.

A:

Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: • Consider the surface given by the equation (r- 1)² + (y+3)2 - (z-2)² = 1. Which of the following…

A: We have to find y- intercept.

Q: Match each equation to the appropriate graph and classify (name) the quadric surface. c. -x2 – y? +…

A: Standard equations of quadric surfaces: a) Ellpsoid: x2a2+y2b2+z2c2=1 b) Hyperboloid of one sheet :…

Q: Identify the type of surface represented by the given equation. x? ? z? 10 =D1 7 O Elliptical cone O…

A: Given query is to find the surface represented by given equation.

Q: Name the surface represented by the equation r2 + z2 = 4 -2z. Justify your answer

A: r2 + z2 = 4 -2z r2 = x2 + y2 Hence, x2 + y2 + z2 = 4 - 2z

Q: Name the surface and draw an accurate Graph of y = x +z? in R'.

A: The surface is an paraboloid. The general equation of a paraboloid that is symmetrical about the…

Q: Write the equation for the above surface.

A: The surface represents the cylinder; with circle in the xz-plane. x2 + z2 = 1  (radius of the circle…

Q: Identify the type of surface represented by the given equation. 2 O Parabolic cylinder O Ellipsoid O…

A: We know that x-h2a2+y-k2b2=1 is the ellipse standard equationGivenx27+y22=2Divide 2 on both…

Q: Given the equation of a circle, x? + y? – 26:t + 6y + 34 = 0, find the coordinates of the center and…

A:

Q: Circle the equation that generates the surface shown below.

A: Solution for 9 (a): The equation that generates the given graph is choice (e): x2+y22=z2

Q: Classify and sketch the surface 12x? – 3y? + 4z? = 12 What are the 3 traces? Show equations of the…

A: A quadratic surface is a hypersurface. It is nothing but the generalization of a conic section in…

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Reduce the equation to standard form, classify the surface and sketch it    4y2 + z2 - x - 16y - 4z…

A: Given: 4y2 + z2 - x - 16y - 4z + 20 = 0

Q: Identify the surface defined by the following equation. 2 y 3 15 The surface defined by the equation…

A: Topic = Geometry

Q: Sketch the surface in R' of the equation presented. 4x² + y? = 36 Interactive 3D Graph - 10…

A: The given equation is, 4x2+y2=36x29+y236=1x232+y262=1⋯⋯1 In 2D, equation (1) is a equation of a…

Q: Identify the surface with equation o = = 7

A: Spherical coordinates: The point Pρ, θ, φ represents a point in the spherical coordinates, where ρ…

Q: 4a. x +4y? +9z? = 36 Name of the surface Y

A: Given:  x2+4y2+9z2=36

Q: Which of the following equation describes a circle on the coordinate plane with a center at (2, -3)…

A:

Q: Describe and sketch the surface in ℝ3 represented by the equation x + y = 2.

A: The graph is a vertical plane ( that is, perpendicular to the xy-plane) that intersects    the…

Q: Express the following equations in standard form to name the corresponding surface and sketch a. x²…

A:

Q: Determine the center and radius of the following circle equation: x +y + 8x + 18y + 72 = 0

A:

Q: Determine the center and radius of the following circle equation: x + y + 4x 6y + 9 = 0

A:

Q: Find the traces for the given surface: 16x? +16y² – 9z = 0. Then sketch and identify the surface.…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x? – 4x + y? + 3 =…

A: Solve for the equation

Q: Identify the type of surface represented by the given equation. x? y? ? O Hyperboloid of two sheets…

A:

Q: Given the equation of a circle, z +y² – 6z + 2y +1=0, find the coordinates of the center and the…

A: The given equation of the circle is x2+y2-6x+2y+1=0

Q: Find the equation and sketch the graph of the surface generated by S revolved about the y-axis.

A: We are asked to find the equation of the surface generated by S revolved about the y-axis. The…

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.