Example: find the maximum and minimum values of the function f(x, y) = 3x + 4y on the circle x +y² = 1 Solution: we model this as a Lagrange multiplier problem with f(x, y) = 3x +4y , g(x,y)=x² +y² –1 and look for the values of x , y, and 2 that satisfy the equations:

Q: the minimum and maximum values of f(x, y) = x²y4 + 5 subject to the constraint x² + 2y² = 6. exact…

A: Maximum and minimum value

Q: vertex of parabola : (-2,1)= (h,k) x=a(y-k)²+h ✓ (-1.5, -2.3) (j,4.2)

A: Given Vertex of parabola h, k=-2, 1 Equation of parabola x=ay-k2+h Points of intersection of line…

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: 3. Use the method of Lagrange multipliers to find the point/s on the parabola y = 3x² that is/are…

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Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: Consider the problem of determining, in an Oxy orthogonal Cartesian system, the equation of the…

A: The objective is to determine the value of m for which the line will be tangent to the circumference…

Q: Use Lagrange multipliers to determine all points on the graph of 3x² + 2y² -z = 0 nearest the point…

A: This is a problem from optimization. It will require using Lagrange's multiplier method to find the…

Q: 2. Given the parabola f(x) = -(x+ 2)² + 4, find the x-intercept(s). x = -2, x = 4 x = 4 x = 0, x =…

A: NOTE: Refresh your page if you can't see any equations. . to find the x-intercepts take f(x)=0

Q: Match the space curves in Figure 1 with their projections onto the xy-plane in Figure 2. *** (i) ()…

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Q: A triangular plate occupies the triangular region D with vertices (1,0), (5,0), and (1,4). The…

A: Given vertices of a triangular region are (1,0), (5,0), and (1,4) and the temperature at each point…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: A rectangular box of length x, width y, and height z has a surface are of 700 cm². Set- up the…

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Q: Solve using Lagrange Multipliers. Then In that same spirit, calculate the exact shortest distance…

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Q: Find the unique quadratic polynomial y = ax² +bx+c that passes through the three points (1, 1),…

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Q: 1. The three points A = (-2, -4), B= (6,2) and C = (-3,3) are taken as the vertices of a triangle T.…

A: Given that: A=(-2, -4), B=(6, 2), C=(-3, 3)

Q: 2 Consider the equation 8y + 3x - 48. The x-intercept is ( ), the y-intercept is ), and the slope is…

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Q: A parabola is defined as being the locus of points P(x, y) that satisfy FP= MP, given coordinates…

A: Formula of the distance of two points x1,y1 and x2,y2 is: d=x1-x22+y1-y22 Here, FP is the distance…

Q: a) X-5 – 1 y+1_z-4 -2 3 And x-3y-2z+2=0 b) d: [x,y,z]-[4,0,-1]+[2.1.-1] And 6x-4y+8z-16=0

A: To determines, if possible, the point(s) of intersection of each line and each plane defined by the…