Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

Q: Use the Lagrange multiplier method to find the point on the surface z = Iy + 10 that is closest to…

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Q: Find the matrix A of the quadratic form associated with the equation. 7x2 + 7y2 + 7z2 + 6xy + 6xz +…

A: We will find corresponding matrix and then its eigen values to determine final equation eliminating…

Q: In Exercises 47-50, verify that Wy %3D Wex- 47. w In (2x + 3y) 48. w = e + x In y + y Inx

A: NOTE-  As per our guidelines we have to solve only first question. Given data- w = ln ( 2x + 3y ).…

Q: Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: Prove that the system of parabola y2= 4a(x+a) is self orthogonal

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Q: Verify that ) Determine from y Graph the solition of the IVP. is a solution of the ODE. . the…

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Q: Draw the bifurcation diagram for i = (x – 3)(c+ x)

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: pivot in the simplex tabléäu. X1 X2 X3 $1 $2 S3 6. 2 4. 4 6. 1 1 6 1 1 1 - 3 1 0 1 e pivot is…

A: In this question, the pivot in the simplex table is determined. Simplex Method A simplex approach is…

Q: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: prove that the system of parabolas y2=4a(x+a) is self orthogonal

A: We show that the family contain both members with slope m and slope -1/m. Hence the family will be…

Q: Below the paraboloid z = 18 – 2x² – 2y² and above the xy-plane -

A: The region D lies below the paraboloids z=18-2x2-2y2 and above the xy-plane.

Q: %3D by the paraboloid z 4-x2-12 =4-x- c.m. R. x +y = 4

A: Given, Solid of constant density δ bounded by R: x2+y2≤4 in plane z=0 and paraboloid z=4-x2-y2 To…

Q: Determine the Jacobian matrix of the function f:R³ → R³ given by f(x,y,z) = (3x²y+ yx²,4x²yz², 6xz³…

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Q: Write an equation for the conic in the xy-plane for - ) 1 at e- 30°. 15 3x° + 42/3xy- 39y² – 360 - 0…

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Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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Q: Find the matrix A of the quadratic form associated with the equation. Then find the equation of the…

A: A quadric surface is a surface in R3 described by a polynomial of degree 2 in three variables:ax2 +…

Q: Use the indicated entry as the pivot and perform the pivoting. $3 z 0 0 60 o ol 80 1 0 300 0 10 X1…

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: prove that the system of parabolas y² = 4a(x + a) is self orthogonal

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Q: Find the solution using LU Decomposition: 7x + 5y − 3z = 16 3x − 5y + 2z = −8 5x + 3y − 7z = 0

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: What are the perpendicular generators on (D) 좋 =3 %3D2 (P) 16 2. of the surface

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Q: 9x2 + 4y? at which the Find the point on the paraboloid z = normal line is parallel to the line…

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Q: Consider AB in the coordinate plane below. 10 4. 2. A -10-9 -8-7 l0 1 -1 -5-4-3 -2-1 2. 4. 10 -2 -3…

A: Given: AB¯

Q: If yi = 1, Y2 = In a are two linearly indepen- dent solutions of ry"+y' = 0, then the partic- ular…

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Q: Find the matrix A of the quadratic form associated with the equation. 3x2 + 3y2 + 3z2 + 4xy + 4xz +…

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Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

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Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

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Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: Find the matrix A of the quadratic form associated with the equation. 6x² + 6y2 + 6z? + 8xy + 8xz +…

A: Given 6x2+6y2+6z2+8xy+8xz+8yz-1=0

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Find the Wronskian of a given set {y1, Y2} of solutions of (1 – a²)y/" – 2ry' + a(a+ 1)y = 0 when…

A: According to the given information it is required to find the Wronskian of solution set

Q: Draw the bifurcation diagram for i = (x – 3)(c + x)

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Q: Use the method of Frobenius to find two linearly independent solutions of the given second order DE.…

A: For solving a differential equation using the Frobenius method, substitute: y=∑n=0∞cnxn+k in the…

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: Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the…

A: A given set of points can be assumed to be on a surface given by an equation when the each of…

Q: Write the given linear system in matrix form. dr dt -3x + 4y + et sin(2t) dy 5x +9z +4et cos(2t) ||…

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Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: 3- Find the orthogonal trajectories of a system. x²y² – 2xya + a = 0 %3D

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Q: Show that the “conic” x2 + 3y2 − 6x + 12y + 23 = 0 has no points.

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Q: (a) If A = x³yi + (xy + yz²)j + xy³k; B = y²zi – 3xz²j+ 2x²yk; ¢ = 3x²y + xyz – 4y²z? – 3 determine,…

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Q: Find the null space associated with the equations: 2x+z+w = 0 7x-6y–z–w-v = 0 -5x+4y+w = 0

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.