What is the vertex of y = Vx + 4+1 O (4, -1) O (4, 1) O (-4, 1) O (-4, -1)

Q: Minimize Subjec to Xx -3 Xq +4 Xz-5 X,- 2X2 <3 2Xx -Xx Z4, XxZ0 and Xg is unnaitaeted

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Q: X + x, + 4x, 9х, = 7 X2 2х, + 6х, 17x, = 5 2x2 4x, + 9x, 25х, 12x, = 4 = 7 4x4 explain the solution…

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Q: Determine ? such that ?′′(?) = 12? − 1 and 1 is both a critical number and a y- intercept of ?.

A: A differential equation is an equation in x,y and derivatives of y.  A linear differential…

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: 5. Show how the origin changes stability as a changes by using the Poincaré Diagram. x - [i :]• 2 a…

A: The stability of fixed points of a system of constant coefficient linear differential equation of…

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: Suppose that Mrs. Jena (in the position of T) want to travel to the top of regions diagonally right…

A: To find the number of route to reach the top of the region :-

Q: Why the 1st row and 1st column of the JACOBIAN MATRX is always Zero ?

A: It is not necessary that the 1st row and the 1st column is  always zero. It may be possible or it…

Q: Find the minimal solution of x+2y-z = 1; 2x+3y+z = 2; 4x+7y-z = 4.

A: Given:

Q: Find the equation of the family of orthogonal trajectories of the system of parabolas y^2 = 2x + C

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Q: Calculate E∫x3dx1dx2dx3, where E is the vertex tetrahedron (0, 0, 0), (1, 1, 0), (1, 0, 0),(1, 0,…

A: The solution is given as follows :

Q: 6. Find the orthogonal trajectories of the family of circles passing through the points (1, –2) and…

A: A Curve is called Orthogonal trajectories if it cuts every member of a given family of curves at…

Q: Sve SVé -3 dt u = Ve' – 3

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: 1. Use agrange multipliers to find the extreme values of f(x,y)=2x²+ y on the circle x² + y² =1.

A: Here, f(x,y)=2x2+y and let g(x,y)=x2+y2, thus, the constraint is g(x, y)=1. So, fx(x, y)=4x; fy(x,…

Q: 6. Find the extreme valucs of f(r,y) = ry subject to the constraint 4x2 + y? = 8 by using the method…

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Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: A 2.25 m -4 m- -e=90° µ=0.1 -3 m 3 m k= 200 N /m- 3 m -2 m-F1 m- 3 m -Inx -3 m- -3 m- F(x). boundary…

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Q: How would I create a tree and find dw/dt of  W = (2x-3y)/(5z-y) x = t, y = -2t,  z = -3t.

A: The tree can be created by using the partial derivative. Here, x = t, y = -2t, z = -3t and…

Q: 6) Use Lagrange multiplier method to find the extrema of f(x1, Xz. -. , In) = x, + x2 + +x, subject…

A: Given, f(x1,x2,....xn)=x1+x2+x3+.....xn,  constraint x12+x22+x32+....+xn2=1 now equation we need to…

Q: Minimize ƒ(x, y, z) = xy + yz subject x2 + y2 - 2 = 0 and x2 + z2 - 2 = 0.

A: We will make use of the method of Lagrange Multiplier. Please see the primer below:

Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: For such a system, there is an invariant curve that joins the saddle point p to itself. Then we say…

A: Note :- “Since you have asked multiple question, we will solve the first question for you. To get…

Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

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Q: How is the Jacobian formulated?

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Q: I want to solve this questionQ) Use Lagrange multiplier to find the largest product of three…

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Q: where a, b, d, e, r and K are positive constants. What type of interaction exists between N1 and N2?…

A: The objective is to state the interaction between N1 and N2. To state the ecological implication of…

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: Calculate the equilibrium point using Gauss-Jordan Elimination only for the case where the number of…

A: The inter species competition scenario can be modelled in terms of standard Lotka Volterra ODE model…

Q: Use Lagrange multipliers to find the maximum and minimum values of f (x, y, z) = x2 + 2y2 + 3z2…

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Q: Find the maximum of the following function: h(x,y) = In(x56 yl4) given the constraints: 4x2 + y? =…

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Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: Given the vectors x and y',..., y™ in R". Our objective is to check whether x E conv{y', . , y™}.…

A: Given:vectors x and y1,...,ym in Rn

Q: round (cov (DFRAME), 2) M N 0 M 2.71 -1.33 0.38 -1.20 0.78 N -1.33 2.89 -1.44 -0.89 0.38 -1.44 5.60…

A: The covariance between two variables say, X and Y is denoted by Cov(X,Y). The covariance between X…

Q: 4. By separating the variables convert the PDE into a system of ODES = u, XX

A: The equation with separable variable is U(x,t)=X(x)T(t) Th partial differential equation of the form…

Q: Minimize the function f(x, y, z) = x² + y² + z² subject to the constraint 6x + 12y + 12z = 54.…

A: We solve by the method of Lagrange  Multipliers

Q: 5. Find the orthogonal trajectories of the family of hyperbolas x² - 2y = ax. %3D

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Q: Compute the Wronskian for 2t^2y''+3ty'-y=0

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Q: For the system * = x + u, ind the set of points that can be steered to the origin x = 0 by an…

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Q: simplex method

A: We have to solve the given problem by simplex method.

Q: У'-у%35х, у(0) -0, у'(0)-1. – y

A: NOTE: Refresh your page if you can't see any equations. . find roots for the homogeneous system…

Q: Minimize Z=8x+12y subject to 4x+6y214, 4x+5y9, x>0, y20 M=?

A: Given LPP is Minimize  Z = 8x + 12y Subject to  4x + 6y ≥ 14, 4x + 5y ≥ 9, x ≥ 0, y ≥ 0

Q: Maximize P = xyz with x +y = 12 and z+y = 12, and x¸ y, and z >0.

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Q: Construct a model for the number of cats, y, after x months that make use of the following…

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Q: Maximize f(x,,x,)= 24x, – x' +10x, – x %3D subject to *; 58 X, 54 x, 2 0, x, 20 and

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Q: 3. Use the method of Lagrange multipliers to find the minimum value of f(1, y) = x* – 2r’y – 4z³ +…

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Q: Find all the local max/min and saddle points for the function f(x, y) = a + y³+3x2 - 3y? – 8

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