A figure is located at (0, 0), (−3, −4), and (−3, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.

Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z2 +…

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Q: + y? )dx + (x² – y²)dy , where C is the triangle with vertices (0, 0), (2, 1), and (0, 1), sitive…

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Q: Find the average height of the paraboloid z = x + y over the square - 3sxs0, - 3sys0. The average…

A: Given: The equation of paraboloid is, z=x2+y2. The limits of the square is -3≤x≤0, -3≤y≤0. The…

Q: Let a > 0 and b > 0. Show that the area of the ellipse x2/ a2 + y2/ b2 = 1 is ab

A: Given that, The equation of the ellipse  x2/ a2 + y2/ b2 = 1 , where a > 0 and b > 0. Solve…

Q: The :. conic section xy a constant .identify (25+ w2) =D2C+ w is

A: The given equation is xy=2x+5y-25+w2, where w is a constant.   We have to identify the type of the…

Q: h the following conic sections: y2 -4y +8-4x = 0 %3D

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Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: 10) (x + 7)²_ (y + 4)² = 1 + 81 36

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Q: ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?

A: While rotating the triangle around x=0 it becomes a cone

Q: Find a rational point on the plane conic 2x2+y? = 6 other than the points (+1,±2). Show all your…

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Q: n and indicate the location of the centroid. Use symmetry when possible and choose a convenient co…

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Q: Which of the following is NOT a method for finding volume of solids of revolution? (A) shell method…

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Q: Describe what kind of conic section is the graph of 5x2 − 4xy + 8y2 − 36 = 0. by using linear…

A: We need to find the nature of the conic section for  the graph of 5x2-4xy+8y2-36 =0.

Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 = 1 can be written as: z² + (…

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Q: w each conic section. +x + 8y + 11 = 0 24) x² + y + 4 = 0

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Q: find a parametrization for the curve. the upper half of the parabola  x-9=y^2

A: The given curve is x-9 = y2  ...(a) Putting y = t in (a) then x = 9+ y2…

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: 2- Paraboloid what is it? explain briefly with images

A: Answer:   As per guidelines we can do only one question at a time so i had answered question 2 below…

Q: The figure below shaws the solid that lies under the parabolaid z= 4r? + 4y? and above the xy-plane,…

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Q: Q.2. Show that the area of the ellipse =1 is z ab. ab

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Q: az Given the ellipsoid = 3 , find (7.0. 2). + 2

A: The equation of the ellipsoid is x2+y22+z22=3We should find ∂z∂x at (7,0,2).

Q: Given hyperbola   x2   −   y2   = 1   9         16       how do you determine the focal length?

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Q: Determine the type of conic: 16. 2x2-4xy + 8y2 +7 = 0 17. 2xy-x + y-3 = 0 %3D %3D

A: The general equation of conics is given as Ax2+Bxy+Cy2+Dx+Ey+F=0, where A,B,C,D,E and F are real…

Q: The figure below shows the solid that lies under the paraboloid z= 2x2 + 2y² , and above the…

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Q: Find a parametric representation of the solution set of the linear equation.x + y + z = 1

A: Consider the given linear equation  x + y + z = 1 We have one equation and three unknown(x, y, z).…

Q: ellipsoid x* + + = 3 z2 n2 q2 r2

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Q: Which of the following is NOT a method for finding volume of solids of revolution? A conic method B…

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Q: Point K is a centroid of the triangle JGI. If KL = 28 cm, what is JL?

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Q: H. Identify the conic sections represented by the following formula a) 2x2 – 8xy + 4x = 12 b) x² + y…

A: I have solved first 3parts only and for all parts solution repost again

Q: 29. A tank full of water has the shape of a paraboloid of revolu. tion as shown in the figure; that…

A: Height is 4 feet and radius at the top is 4 feet So the parabola passes through the point (4,4) The…

Q: 3. The point D is the centroid of AABC. Find the value of the distance DC if : GD = 2x – 8 and GC =…

A: It is known that the centroid of a triangle is the point at which the 3 medians of the triangle…

Q: 4. Find the area of the largest isosceles triangle that can be inscribed in the ellipse y2 = l. a2…

A: To find the area of the largest isosceles triangle.

Q: Identify the type of conic from the discriminant. y-2 = 0.0=45" ANSWER: Blank 1 Blank 1 Add your…

A: Check discriminant b^2-4ac is less than zero, greater than zero and is equal to zero.

Q: find a parametrization for the curve.  1.the lower half of the parabola x - 1 = y2 2. the left half…

A: (1)Find the parameterization for the parabola equation

Q: As an engineer at Ghana Atomic Energy, you have been tasked to design a cooling tower in the shape…

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

Q: (1, 9) € R? :- 25yS1,-1SIS 2}

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Q: Using the property of Re z and Im z to show that the hyperbola x2- y2 = 1 can be written as: z? +…

A: We know that x=Re(z)=z+z2 and y=Im(z)=z-z2i. We are given the equation of hyperbola x2-y2=1.

Q: 1. Classify the equations below according to the type : * i) Uxx- 2uxy – 2uy = 0 O hyperbolic O…

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Q: 4) The solid lies between planes perpendicular to the x-axis at x = 0 and x = 6. The cross sections…

A: Given: y=-5x  to the parabola y=5xAs we can see in the diagram is given below.

Q: Identify the type of conic from the discriminant.*2 + 2xy +y² + /2x - /2y– 2=0, p=45° ANSWER: Blank…

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Q: Q;:Draw the graph of the conic section 5x2 + 4xy + 2y² = 36. %3D

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

A: Given, the below figure :       A lamp is located 3 units to the right of the y-axis and a shadow…

Q: the region bounded by the graph y = 3x - x3, the y axis, and the line y = 2 is revolved about y…

A: C.

Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

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Q: 2. Find the orthogonal trajectories of the ellipses 4x² +y? = 3x. 3. Determine the isogonal…

A: The given equation of  the family of ellipses is  4x2+y2=3x           (i) Differentiating (i) w.r.t…

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 1 can be written as: z? +…

A: See the attachment

Q: Find the area of the fundamental rectangle of the hyperbola. x2 − y2 − 6x − 8y = 8

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Q: Q9. Draw a sketch of a hypersphere in four dimensions.

A: Hypersphere :''Hypersphere''  the mathematical object that live on the sphere in 4 dimensional…

Q: Find the area enclosed by the ellipse x2  / a 2    +   y2   /b 2    =1

A: Given ellipse is The ellipse meet x-axis at points (-a,0) and (a,0) and y-axis at points (0,-b) and…

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.