Find a simple closed curve Cwith counterclockwise orientation that maximizes the value of C3 4x: O isa circle of radius 2 with the center at (2, 2). O Cis the triangle with vertices (0, 0), (2, 0), and (0, 2). O Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2). O The integral doesn't depend on the form of C. O Cisa circle of radius 2 with the center at the origin.

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: AJKL has coordinates J (2, 4), K (3, 1) and L (3, 3). A translation maps the point J to the point J'…

A: Explanation: Given that, △JKLJ(2,4)→J'(3,3)K(3,1)L(3,3)     Concept Used: To translate the given…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 9x² + y² = 6. maximum value=…

A:

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1),…

A: Let Put the given points in f we have Now, we have minimize this function.

Q: Trapezoid PGRS with vertices P(-6, 2), G(-2 -0, R(-2 -3), and S(-6, -6), reflect in the linex-1 (4)…

A: We need to draw transformed image.

Q: irst part of question is that Find the locus of a point such that the sum of its distance from the…

A:

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Q1/A- Find the center and radius of the sphere have equation x + 2x + y²-2y + 2²-6z=14. B- Find the…

A:

Q: Use Lagrange multipliers to find the points on the sphere ² + x² + y² − 2y − 10 = 0 closest to and…

A:

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

A:

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

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: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: P(x, y) is any point on the ellipse 16x\power{2} + 25y\power{2} = 400 and F\index{1}=(3,0),…

A: We have 16x2 + 25y2=400         or      x225+  y216=1        or       a2=25 and  b2=16

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

Q: 17. [Shadows] Consider the parallelogram surface whose vertices are (0, 0, 1), (2,0, 1), (3, 2, 1),…

A:

Q: $ x4* dx + 2x*y dy where C is the triangle wl vertices (0,0), (3=), and (2, 4) i ?

A:

Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

A:

Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² 1² 49…

A:

Q: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

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

A: To Find: All points on the graph of 3x2+2y2-z=0 that are nearest to (0,0,2) using Lagrange…

Q: B) The line passes through the point (2,4,5) and perpendicular to the plane 2x+y- intersects the x-y…

A: Given that the line passes through the point (2, 4, 5) and perpendicular to the plane 2x+y-5z =21

Q: 2 = 2x2+y that are Use Lagrange Multipliers to find the points on the cone closest to the point (-6,…

A: