This exercise refers to the hyperbolic paraboloid z = y – 3x2. Find an equation of the parabolic trace in the plane x = 2. %3D O z2 = y + 12 = - y+ 3 y = z + 12 %3D = z – 12 – z – 6 %3D

Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: 1. Consider the ellipsoid x² + y² + 4z? = 12. (a) Find an equation of the tangent plane to the…

A: As per bartleby guideline for more than one question, only 1st one is to be answered. Please upload…

Q: Calculate | [(a4 – 3y) da + (2y³ + 4.x) dy] wherein r(t) = (3cos(t), 3sin(t)), 0 <t < 27, is an…

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Q: The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. Find the points on the ellipse…

A: The plane x + y + z = 1 intersects the cylinder x2 + y2 = 1 in an ellipse. Find the points on the…

Q: This exercise refers to the hyperbolic paraboloid z = y – x'. (a) Find an equation of the hyperbolic…

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Q: Given the surface 9x^2 − 4z^2 = 9y. Find its traces on each coordinate plane and on the planes y=4,…

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Q: This exercise refers to the hyperbolic paraboloid z = y - x. (a) Find an equation of the hyperbolic…

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Q: The following system of equations describes a shape in R³ using cylindrical coordinates. r = 1 Z = 0…

A: Relation between cylindrical co-ordinates and rectangular co-ordinates is given as  x=r cosθy=r…

Q: z' +z+1 Evaluate -dz , where C is the ellipse 4x + 9y = 1. c z² – 3z+2

A: By Cauchy integral theorem,            If the function fz in analytic in some simply connected…

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: The figure below shows the solid that lies under the paraboloid z = 4x? + 4y?, and above the…

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Q: e |/| e² dV where E is enclosed by the paraboloid z = 4 + a?² + y², the cylinder Evaluate 2² + y² =…

A: Here we have to evaluate ∫∫∫Eez dV  where E is enclosed by the paraboloid z=4+x2+y2, the cylinder…

Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

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Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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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: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…

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Q: This exercise refers to the ellipsoid 36x + 4y² + 72z² = 288. Find an equation of the elliptical…

A: For getting elliptical trace, substitute the plane equation in ellipsoid equation.

Q: te the surface integral /| (32zi + 2zyj+ 2yzk) · ds S is the part of the parabola z = 15 – x² – y…

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Q: (b) f(x, y) dA where D lies below the paraboloid z = x2 + y?, above the ry-plane, and inside the %3D…

A: Let's find.

Q: 'Use Cartesian coordinates to evaluate III y² dV where D is the tetrahedron in the first octant…

A: We have to use Cartesian coordinates to evaluate Volume where D is the tetrahedron in the first…

Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: This exercise refers to the hyperbolic paraboloid z = y-x. (a) Find an equation of the hyperbolic…

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Q: This exercise refers to the hyperbolic paraboloid z = y -x. (a) Find an equation of the hyperbolic…

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Q: This exercise refers to the hyperbolic paraboloid z = y - x. (a) Find an equation of the hyperbolic…

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Q: Identify a generating curve on the xz-plane for the surface of revolution with equation a² + y? + 2?…

A: Consider the surface of revolution with equation, x2+y2+z2=e2x it is required to find the generating…

Q: Find the value of ∫∫s(x^2y^2z^2)dS correct to four decimal places, where S is the part of the…

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Q: Q1/ (A) If w= (x?+yz+Z?). Find m such that W = Wxx + Wyy + Wzz=0 Ans. n= -//2 %3D (B) Use Lagrange…

A: (A) Let w=x2+y2+z2m ⇒wx=∂∂xx2+y2+z2m⇒wx=mx2+y2+z2m-1∂∂xx2+y2+z2⇒wx=mx2+y2+z2m-12x Now find wxx.…

Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: Ex.9. An ellipsoid y2, z2 = 1 is surrounded by a luminous a? b2 ring x = 0, y2 + z² = a². Show that…

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Q: This exercise refers to the hyperbolic paraboloid z = y - x?. (a) Find an equation of the hyperbolic…

A: To find the following sub parts of the given question :-

Q: 17. Evaluate F · dš if F(x, y) = (y*, 2xy*) and & is the ellipse x? + 2y? = 2 (with counterclockwise…

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Q: Use Cartesian coordinates to evaluate y² dV where D is the tetrahedron in the first octant bounded…

A: Let us consider a triple integral of the form ∫ab∫f(x)g(x)∫h(x,y)r(x,y)F(x,y)dzdydx To solve the…

Q: The surface x2+y?+z?-4x-2z+5=0 is: O an elliptic paraboloid O a point O no graph O a hyperboloid of…

A: Please see the below picture for detailed solution.

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

A: Consider the given equation x - 1 = y2 By adding 1 from both sides, ⇒ x = 1 + y2 Let, substitute y =…

Q: Is it true or false that by using a suitable translation x = x' + xo, Y = y' + Yo, it is possible to…

A: Transforming the conic equation

Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

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Q: This exercise refers to the hyperbolic paraboloid z = y? - x². (a) Find an equation of the…

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Q: This exercise refers to the hyperbolic paraboloid z = y? – x². (a) Find an equation of the…

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Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: The perimeter of an ellipse is given by P = 4a V1-k-sin-8 de where, k = Using the Simpson's rule,…

A: The given equation of the ellipse is: x242+y272=1 Result: The standard form of the ellipse is:…

Q: This exercise refers to the hyperbolic paraboloid z = y? - x?. (a) Find an equation of the…

A: Solution

Q: Find equetion of Hhe parabole farmm an I with focus zt (3,0) and divectrix x=-3

A: Focus =  F= (3,0)  Directrix - x =-3  i.e. x+3=0

Q: 2. Find the area of the ellipse S on the plane 2x + y + z = 2 cut out by the cylinder x2 + y? = 2x;…

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Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: = r² at r = 1,0 = 4. Write the linear approximation of the paraboloid z=

A: The given paraboloid is z=r2. To find: linear approximation of the given paraboloid.