Consider the equation system: y2 + w2 − 2xz = 0 x3 + y3 − z3 + w3 = 0 Prove that exists surrounding neighbourhood of point P = (1, −1, 1, 1) in which the solution (x, y, z, w) can be written with x and z as functions of (y, w)

Q: = Let -3 -1 -~--~--~--~--~- , V3 -5 1 , V₂ 2 0 combination of V₁, V2 and V3. 5 -26 , V4 -9 -1 -3…

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Q: Which equation has x-intercepts of (3, 0) and (7, 0)? O y = z + 10z + 21 O y = r- 10x + 21 O y = 12…

A: (3,0) and (7,0) satisfy the required equation

Q: a point Q(x2, y2) is on the line segment passing through R(-2,5) and S(4,1). Find the coordinates of…

A: Given: Given that the point Qx,y is on the line segment passing through R-2,5 and S4,1 Point Q is…

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A: Since you have asked multiple questions in a single request, we would be answering only first…

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Q: (1,6) and perpendicular to 2x+7y=1

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Q: Find all the possible points of intersections of 9x2 + 4y2 + 18x – 16y = 0 and (x + 1)2 + (y– 2)² =…

A: Given curves: 9x2+4y2+18x-16y=0   ········(i)x+12+y-22=5         ········(ii) From equation (ii)…

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Q: The equation of OP is (x- 3)+ (y- 1)²=9. Without graphing, explain how you can determine whethen che…

A: Given equation of circle is, x-32+y-12=9

Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: Suppose you are climbing a hill whose shape is given by the equation z = 2000 - 0.005x²-0.01y2,…

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Q: Find the equation y = f(x) passing through the points (-11-21), (1,15), (2,12) and (3, 3)? Find also…

A: We will use the Lagrange interpolation method. We have: x x0=-1 x1=1 x2=2 x3=3 y y0=-21 y1=15…

Q: Find the values of x and y for which (x + y, 0) = (3,1 - y)

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Q: find x and y if (2x+1,y)=(5x+4, -7)

A: Given: 2x+1,y=5x+4,-7

Q: Linearize the non-linear equations: 1. y= a+ bx+cx^2 2. y=x/(a+bx) + c

A: According to the given information it is required to linearize the given non-linear equations.

Q: Find all points that simultaneously lie 3 units from each of the points (2, 0, 0), (0, 2, 0), and…

A: Let such a point is (x,y,z)

Q: The graph of the linear equation r=y passes through the point: O (4, 4) O (4,0) O(0,-4) O (4,-4) O…

A: Given equation  x=y

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Two linear functions, y1 and y2 have been defined and the graph of y1 - y2 has been graphed in an…

A: Given: Two linear functions y1 and y2 have been defined and the graph of y1-y2 has been graphed in…

Q: Q: (2x+y)(x+y) ах Find -?

A: Given query is to find indicated partial derivative.

Q: а a²-x² ху(х + у)dydx 0. x,

A: Integration of function expression with respect to variable x or y gives the area under function…