Consider uxx + auxy – 2uyy + ux + 2uy = 0 Find all values of a so that the PDE is Hyperbolic.

Q: De termine an equanion for the line of intersechon of the following planes 3x+2y +5z = 4 and 4x-3y…

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Q: Consider AABC with its centroid at point G and median at BH. What is the length of GH if BG = 3x + 4…

A: Given Data: The length of BG is: BG=3x+4 The length of GH is: GH=x+10 The ∆ABC with its centroid at…

Q: 36 Find the equation of the tangunt Hne plane at l'2,1) and f L1.95, to fxiy) = Jao-xa - Tya %3D use…

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Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

Q: Consider the quadric ax2 + y2 + 4z2 + x + 6y−4z = −a−10 where a is a parameter. Find all the values…

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Q: B. Sketch these Cartesian products on the x-y plane R² (or R for the last two). 9. {1,2,3} x…

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Q: E. Determine the set of points satisfying the condition described by |z – 2i| + |z + 4i| = 10. Then…

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: Evaluate S. F·dr, if S'is the portion of the paraboloid z = 4 – x² – y² for which z 2 0 and F(x, y,…

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Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

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Q: Show that the value of ∮C xy2 dx + (x2y + 2x) dy around any square depends only on the area of the…

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Q: Uxxtuyy-Uzz+6ux-0 is parabolic O hyperbolic O elliptic O

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Q: Frned the poind al on 2x+y + 2' =4 n hreh bangend plana アaralle l lo tk plane x-2y +62 =5. is

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Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

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Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

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Q: Evaluate Sf,(z+ 3y – x²) dS where S is the portion of z = 2 – 3y + x² that lies over the triangle in…

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Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

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Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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Q: Consider the following semilinear first-order PDE ди ди + Y = xe¯u ду (i) Find the general solution…

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Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

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: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: Find i x w if ||T|| = 3, ||w|| = 4, 0 = and ī, w both lie in the xz-plane (as shown). 3 %3D

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Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

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Q: 3.2. let f(x) = 2, x+4 xez, * 1 - 1 1/2/20 -74x45 -*>$ Approximate the foldoy using Trapezoid mule…

A: In order to approximate the integral: ∫abydx, the trapezoidal rule uses the formula:…

Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

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

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Choose a set S of four distinct points in R3 such that aff S is the plane 2x1 + x2 – 3x3 12. Justify…

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Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: c. Let P(x, y) = y² + sin¬1 x² and Q(x, y) = 2xy + 4x. Suppose that C is the parallelogram with…

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Q: Find the average haight of the Paraboloid z- xry* over the square osx <2, osd<2

A: We need to find the average height of paraboloid

Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

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Q: Let P be the plane 2r + u – 7 = 2 and let 0(1.0.3) be a poir

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Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

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Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

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Q: 3. Find all the roots of z³ + 1 = 0 and sketch them on the Argand plane

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Q: OFind the orthogonal Tradectories of the families of y2-5ax 42 - %3D where a being a Parameto

A: For find the orthogonal trajectory replacement of dy/dx with (-dx/dy) is required.

Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.