Simplify and identify the quadric surface, given: 9x2 – 18x + 4y² + 16y – 36z + 25 = 0

Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

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Q: Find the standard equation of the sphere with center C and rad C(1, v2, -5); r= 3

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 12x - 4y + 4z + 35 = 0 Find its…

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Q: (a) Identify and graph the quadric surface -r - y + 2? = 1.

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Q: Find the center and radius of the sphere. x2 +y2+z2 - 16x - 12y + 6z = -45

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Q: Build a surface and determine their appearance (name).-4x2+12y2-3z2+24=0

A: Find the surfaces for x = 0, y= 0 and z = 0.

Q: identify the following quadric surface x^2/6 + y^2/6 + z^2/16 =1

A: This question is related to Quadric surfaces, we will solve it using given information.

Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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

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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…

A: The given equation is z22-x28=y2. As we know that the general equation of the parabolic cylinder is…

Q: Consider the following equations of quadric surfaces: z =+-4 y? b) 4x² + (2) - - 2z? = -1 %3D | 16

A: The quadratic surfaces are given below-

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: 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: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: Simplify and identify the quadric surface, given: 9x – 18x + 4y² + 16y – 36z + 25 = 0

A: The given function is- 9x2-18x+4y2+16y-36z+25=0

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

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Q: Find the center and radius of each sphere. Sphere: x? + y? + z² – 10x - 8y + 6z = 0 Center: Radius:…

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Q: Identify the quadric surface with equation -a + 9y? – z = 0. O elliptic paraboloid O hyperbolic…

A: given  -x2+9y2-z=0

Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Identify the type of surface (in space) given by the equation, and sketch the surface. a. x^2+y^2=25

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the center and radius of the sphere: x^2+y^2+z^2-8x+2y+4z-9=0

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Q: The distance between the centers of the following two spheres: x²+10x+y²+14y+z²=-73,…

A: Given that: x2+10x+y2+14y+z2=-73      .......(1)2x2-4x+2y2+2z2+8z=-5     ........(2)

Q: Find the equations of the sphere through the circle x + y +2 =1, 2x+ 4y+5z= 6 and touches the plane…

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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

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Q: Identify and choose the appropriate quadric surface. 36z = x + 6v

A: First try for different values of x,y,z and see where the graph lies.

Q: Find the center and the radius of the sphere. x2+y2+z2+3x+3z=

A: See the details solution in below

Q: - The surface 5x^2 + 2z^2 = 3y is heading towards which axis? - Identify the surface generated by…

A: 5x^2 + 2z^2 = 3y x= 3n1 ,  y = -3(5n12 + 2n22) , z = 3n2

Q: The solid that is the common interior below the sphere x + y + z = 80 and above the paraboloid z =…

A: We need to find the upper limit for the given integral.region is bounded below by the sphere and…

Q: 9a2 + 4y? + 36z? = 36 %3D

A: given surface 9x2+4y2+36z2=36 claim- to find the trace of given surface in planes x=k , y=k , z=k ,…

Q: Determine the center of the sphere x2+y2+z2+8x+6y+10z=0.

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Q: Name the surface and graph the given equations in R’: . z+x = 1 b. 2x+3y = 6 с. у%3Dsin x d. z =1- y…

A: (d) Given z=1-y2 we write it as y2=1-z This is the equation of a parabola. For plotting it, we make…

Q: Write the equation of the sphere in standard form. x2 + y2 + z? + 6x – 2y – 2z = 14 Find its center…

A: Consider the equation of a sphere : where a,b,c are coordinates of the center of circle from the…

Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

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: Find the center and radius of the sphere x2 + y2 + z2 + 3x - 4z + 1 = 0.

A: The given equation is x2 + y2 + z2 + 3x - 4z + 1 = 0.   The Standard Equation for the Sphere of…

Q: Consider the equation 4y^2 + z^2 − 4x − 8y + 4z + 8 = 0. Then classify the surface it represents…

A: Given equation of surfaces 4y2+z2-4x-8y+4z+8=0

Q: Identify the quadratic surface, explain the shape and describe the traces. 1. a) z = -sqrt…

A: Identify the quadratic surface,Explain the shape and describe the traces.a) z=-2-x2-y2b) x2+z22=1c)…

Q: Identify and sketch the surfaces in space, 3-D. x² +y² = a² a) b) z = 4– x² – y² x² + y? - z? = 0 |

A: a)  x²+y² = a²

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

A: Answer

Q: Identify and choose the appropriate quadric surface. 121z – 36y – 121x = 43

A: Given, 121z²-36y²-121x²=4356---------equation 1

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

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Q: Write the sphere in standard form. x + y + z? 6x + 2y – 2z = 14

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Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

A: The quadric with equation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10 where a is a parameter. We need to…

Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

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Q: Which surface has the following equation? x2 – 2y = 32 O Cylinder O Plane Paraboloid Hynerboloid

A: Please refer to the image below

Q: Which quadric surface is this? y x2 Elliptic Paraboloid O Hyperboloid of Two Sheets O Elliptic Cone…

A: We have to answer the given equation is of which quadric surface.  given    we can see that its…

Q: Find the surface area of a quarter of the sphere x? + y2 + z2 = 4.

A: The equation of a sphere centered at x0, y0, z0 is defined using the formula: x-x02+y-y02+z-z02=r2,…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.