Describe the surfaces in words and draw a graph. Your description should include the general shape, the location, and the direction/orientation. a. (y + 1)? + (z – 2)² = 9 b. y = 5 c. z = x + 2

Q: Identify the equation associated with each graphed surface. (a) O 22 = - x? – y? + 1 O22 – 1 = y + x…

A: Given graph is  (a)                                                      from graph we observe that…

Q: Graph and identify the shape of the following surfaces given by the following equation (as well as…

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Q: Describe the surface with equation x² + y? +z? + 10x + 4y + 2z – 51 = 0 The surface is a sphere with…

A: solution:-x2+y2+z2+10x+4y+2z-51=0complete the…

Q: Graph and identify the shape of the following surfaces given by the following equation (as well as…

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Q: 3) Describe the 3-D surfaces in words and draw a graph. Your description should include the shape,…

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Q: Select a correct name for this surface and point out the lowest point. O A cylinder, (-1,2, – 1) O A…

A: As we already know that each cross-section of a vertical cylinder of the form z-c=(x-a)2+(y-b)2 is…

Q: 18 What is the equation of a circle with radius 3 and center (3,0)? A x² +y? – 6x = 0 B. x? +y? + 6x…

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Q: Q5 Sketch the surface whose equation is given by (2 – 2)° = (2x² + 4y°).

A: We will use basic of graph plotting.

Q: What is the equation of a circle with center (-5, 4) and radius V2? ㅇ (2+5)2 + (y-4)2 =2 ㅇ (2+ 5)2 +…

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Q: Given -2-x2 -,2 = 1 (a) Write the equation above in standard for (b) Identify the surface. (c) What…

A: Given that: z2-x2-y2=1

Q: Match the equations below with the pictures of the of the level surfaces they represent. 1. 2 – 3x2…

A: B  1. 12z2-3x2-y2=-1

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹ x² + y² O 3 4 y x

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Q: Find the points of intersection of the curves. Then sketch their graphs on the same Cartesian plane.…

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Q: 3. 4x+y 4

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Q: Describe the traces of the surface in the given planes. See Example 2. y2 + z? - x2 = 5

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Q: Let h, k, r, m, n be constant and m, n> 0. A possible graphical representation for the surface of (y…

A: Given Equation:      r-z -y-k2n2 = x-h2m2

Q: x² + + =1 y2 9. 4

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Q: The figure shows a lamp located three units to the right ofthe y-axis and a shadow created by the…

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Q: Sketch the given surface (x/4)^2 + (y/8)^2 + (z/12)^2= 1

A: Given: x42+y82+z122=1

Q: Sketch the given surface

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

Q: Consider the following equation of a quadric surface. a. Find the intercepts with the three…

A: Let a three variable equation fx,y,z=01 x - intercepts when y=0=z2 y - intercepts when x=0=z3 z -…

Q: Describe in words the surface whose equation is given. p = 7 O a circular cylinder with radius 7 and…

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Q: 4. What is the equation of a circle with radius 3 and center (3, 0)? A. x2 + y2 – 6x = 0 B. x2 + y?…

A: equation of the circle with radius 3 and center (3, 0) :(x-3)2+(y-0)2 = 32

Q: Consider the following equation of a quadric surface. 400 400 a. Find the intercepts with the three…

A: The given equation of a quadratic surface                   y2400-x2400=z ⋯⋯⋯⋯⋯ (1) To find     The…

Q: 3a? + 3y? – 30æ – 18y – 6 = 0 is the equation of a circle with center (h, k) and radius r for: %3D…

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Q: (a) What does the equation y = x represent as a curve in R?? O ellipse O cirde O hyperbola O…

A: We want to find true options.

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: a) Sketch (hand drawn) the intersection of y? + z² = 25 and x = 3 in 3D. b) Also, describe the the…

A: When two surfaces intersect each other, a new curve is formed. The curve is referred to as the curve…

Q: Identify the equation associated with each graphed surface. (a) O z? – 1 = y? + 2? O 22 + y² = z O…

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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: 5) Classify the surfaces, listing shape, location, and orientation: a. 4(x-1)2 + 9y+1)² + z² = 36…

A: Given:  4(x-1)2+9(y+1)2+z2=36 ⇒4(x-1)236+9(y+1)236+z236=1⇒(x-1)29+(y+1)24+z236=1 This is of the form…

Q: Sketch and describe the surface created by p=2 csc(ø).

A: Coordinate systems are used to represent a point in three dimensions. The cylindrical-coordinate…

Q: Identify and sketch the section of the surface at x = 0. 2y? - x + 2z = 32 %3D Type of the surface:…

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Q: Identify the following surfaces and sketch your graphic: A)4x² + y²-2y+9Z-35=0 B)y² + 4z² =x

A: Quadric Surface: A graph of a function of two variables z=fx, y is called a quadric surface. There…

Q: Consider the following equation of a quadric surface. x y 49 + 324 a. Find the intercepts with the…

A: Answer

Q: x = z? + y? Name of the surface

A: x=z2+y2 We need to name the surface.

Q: 3 2.59 Describe the surfaces defined by the following equations. a. p = 13 0=25 b. 0= c. 9=4

A: We have to solve given problems:

Q: Consider the following equation of a quadric surface. y? z? =D1 25 2 - 25 25 a. Find the intercepts…

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Q: Which of the following is the graph of the surface whose equation is given by -x2 + y² + z² = 1? a.…

A: Given equation: -x2+y2+z2=1

Q: Identify the name and sketch the following surfaces. i) 3y=9-5x ii) x+y =25-z

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Q: 24. What is the equation of a circle with the center at (1, 3) and a radius of 2 units? a. (x – 1)2…

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

Q: What are the points of intersection between the graphs of the circle and parabola? x² + y? = 37 x² =…

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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: Name the surface and draw an accurate Graph of y = x² + z² in R'.

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Q: The Weingarten map is also called the shape operator. Why does this name make sense? What does the…

A: To Explain: what does the name Weingarten map make sense and what does it tell us about surface .

Q: raph and identify the shape of the following surfaces given by the following equation (as well as…

A: The equation is x29+y225+z24=1

Q: Identify the following surfaces and sketch your graphic: A)4x² + y²-2y+9Z2-35=0 B)y² + 4z² =x

A: We will standardize  given equations 1st and then find required surface ,

Q: Write the equation and determine the type of surface obtained by rotating this line around the…

A: When we rotate the given equation around y axis, we got hyperboloid:

Q: Identify and sketch the section of the surface at x = 0. 16 16 Type of the surface:

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Q: Evaluate and C₂ dz where C is the closed contour shown in the figure below. (Hint: Express C as the…

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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.