Find the largest and smallest outputs of f(x,y)=x2+2y2 on the weird slanted ellipse g(x,y)=x2+y2+xy=3

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

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Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

Q: 14. x + y -4x-12y-129 0 Standard Form: Center: 2,) :(2,6) Radius: \3

A: Steps are shown just try to have (a±b)2 , by substituting any number by substraction and addition.

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: x' = y y' = -6x – 5y (1) Find all straight line trajectories for the system above, using any method…

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Q: Sketch the surfaces ASSORTED 4y2 + z2 - 4x2 = 4

A: Given:  And can be written as,  Therefore, The obtained function is in the form of Hyperboloid…

Q: Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the…

A: Given: f(y)=y2(9−y2)  To find: Solution

Q: A motor and geartrain used in a servo system are operated with a steady voltage and the output of…

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y + = 3 and the paraboloidz =…

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Q: Find the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

Q: Solve using L-U Decomposition Method 1. 4x + 2y + z = 11 -x + 2y = 3 2x + y + 4z = 16

A: The solution is given as

Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

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Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Derive the orthogonal trajectories of the family of hyperbolas ??=?.

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Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find the minimum and maximum distances between the sphere r²+y²+z² = 9 and the point (2, 3, 4).…

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Q: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: ) Find the general solution in terms of real functions. From the roots of the characteristic…

A: Given below clear explanation

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

Q: For the system: = y(2+x – x²) and %3D (2 + х)(у — х) dt a. Find all the critical points. b. Plot the…

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Q: Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points…

A: The equation of the surface given is as follows: 4x2-9y2=9z2+4 (3) The graph of the traces obtained…

Q: x' 3D За — 2у + e"siny 4х — у +е Vsin x

A: In this question,  we find the linearization of this system near the critical point (0,0) by using…

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: A space probe in the shape of the ellipsoid 4x + y +4z = 16 enters the earth's atmosphere and its…

A: To determine the hottest and coldest points on the probe's surface.

Q: Consider the system 3r – 1 Find the critical points of this system. Determine the nature of the…

A: The given system is:

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

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Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Transform the problem for the second-order linear DE y" + 3ty' – y = 1+ sin(t), y(0) = 0, y'(0) = 2.…

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Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.