In Exercises 23–40, determine the center (or vertex if the curve is e parabola) of the given curve. Sketch each curve.

Q: ) Use shifting graph to sketch a) y+2 =|-3 + vx| b) y = -1+ 5sin (2x)

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Q: Exercises 25-28, find the slopes of th- clinationr itions

A: Here we have to find the slope of the line.  Given that, the Inclination of the line is θ=176.2°

Q: In Exercises 40 through 43, consider the problem of fitting a conic through m given points P1(x1,…

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Q: Draw the figure and find the image of the rectangle with vertices A(−4, 2), B(2, 2), C(2, −2) and…

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Q: In Exercises 1-18, graph each ellipse and locate the foci. = 1 4 2. 1. 16 + 25 16 3. 9 36 4. 49 5.…

A: To graph the ellipse and locate the foci. 1) x216+y24=1 Major axis is x-axis and the minor axis is…

Q: 3. Find the coordinates of the vertices after a 180° rotation about Y.

A: our objective is to find the required coordinates

Q: In Exercises 5 to 8, draw the graph of each equation by using the method of Example 3. 5. y = 2x - 3…

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Q: Find the coordinates of the vertices of each figure after the given transformation. reflection…

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Q: Graph the circles whose equations are given in Exercises 24–26. Label each circle’s center and…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Create one model or figure for a Poinrcare Upper Half-Plane model of hyperbolic geometry.

A: As per the question we have to construct a model for a Poinrcare Upper Half-Plane model of…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: In Exercises 51-54, graph each equation. 51. y = 5 (Let x = -3, -2, –1, 0, 1, 2, and 3.) 52. y = -1…

A: Given:

Q: in exercises 37-50, find the vertex, focus, and directrix, of the parabola. then sketch the…

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Q: In Exercises 31–40, write the standard form of the equation of the circle with the given center and…

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

Q: 80. Give an example of the reflective property of a parabola.

A: We have to give some examples of the reflective property of a parabola.

Q: Show that the points A(3,-2,4)B(1,1,1,) and C(-1,4,-2) are collinear

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

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

Q: Create one model or figure for a Klein-Beltrami model of hyperbolic geometry.

A: To create: One figure for a Klein-Beltrami model of hyperbolic geometry.

Q: 9. Reflect a figure with vertices A(1, 2), B(3, 6), C(-1, 2), and D(-2, – 2) across the x-axis. Find…

A: To find the reflection of the given figure

Q: In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation.…

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

Q: 16. х2 — 2х — 4у — 7 %3D 0

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Q: Graph the first-octant portion of each plane.x = 5

A: We have the given equation of plane as x=51x+0y+0z=5            ⋯⋯1 Since, we need to plot the graph…

Q: Derive the system of equation needed for find the four-point Gauss- Legendre quadrature rule.

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Q: Draw the figure and find the image of the rectangle with vertices A(-4, 2), B(2,2), C(2, –2) and…

A: Here Given corner Points of rectangle  are by  A(-4,2) ,B(2,2), C(2,-2) and D(-4,-2) Here scale…

Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel…

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Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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Q: The points, if any, at which a graph crosses or touches thecoordinate axes are called______

A: Axis is the line that forms the framework for a graph. the horizontal axis is called the x-axis, the…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Graph the image of trapezoid RSTU after a rotation 180° counterclockwise around the origin. 104 5

A: Given that:

Q: In Exercises 23–40, determine the center (or vertex if the curve is a parabola) of the given curve.…

A:

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Graph each equation in Exercises 11-26. Let x = -3, -2, -1,0, 1,2, аnd 3. 11. у — х? — 4 12. у 3 х?…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: What are the coordinates of the image of vertex F after a reflection across the line y = -x? O (-1,…

A: Given: Vertex F=(1,-3) To find: Reflection across y=-x and new vertex F'=??

Q: What is different about the shape in part c?

A: Part (c) is a rectangular shape .

Q: Find the lengths of the curves in Exercises 1-2. If you have a grapher, you may want to graph these…

A: Concept:  For y = f(x) in the Cartesian coordinates defined on interval a,b  The curve length is…

Q: Use the result in Exercise 24 to find the equation of the circle that has center (0, 0) and contains…

A: Given Center coordinates of circle =0,0 Point passes through circle=3,4

Q: Use the result in Exercise 26 to find the equation of the circle that has center (0, 0) and contains…

A: Given Center of circle is at (0,0)   and contains point (3,4)   To evaluate, equation of circle

Q: Which kind of symmetry do all of these figures have?

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

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Q: Section 2.6 in Volume 3 1. Draw one crosscut for a fixed z value, one crosscut for a fixed y value…

A: We will solve this question by fixing x, y, and z one by one.

Q: 6. Find an equation of the sphere that passes through the origin and whose center is (3, 1, 3).

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Q: 8. Find the best parabola to fit the data points: (-1, –1), (0, 1), (1,0), (2, 3).

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Q: (a) Sketch the graph of y = a/ for a = ±1, ±2, and ±3 in a single coordinate system.

A: Draw the graph of the function by using the steps: Set the scale for the graph and label the x and…

Q: Sketch and determine the center, foci and vertices of th equation of x2 (y-4)2 + 36 = 1. 49

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Q: Which figure will this net make?

A: We have to decide the shape.

Q: Use a graphing device and the result of Exercise 25(a) to draw the triangle with vertices A(1, 1),…

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Q: Write a MATLAB code to find the equations of the tangent lines of the ellipse x2 + 4y2 = 36 that…

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Q: Which of the following is a net of the above cuboid?

A: Net of the cuboid is in option (A)

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.