Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this minimum distance?

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Use the method of Lagrange multipliers to find the minimum distance from the origin (0, 0) to the…

A: We need to use the method of Lagrange's multiplier to determine the minimum distance from the point:…

Q: If ƒx(a, b) = ƒy(a, b) = 0, does it follow that ƒ has a local maximum or local minimum at (a, b)?…

A: To determine: Whether the function f follows that it has a local maximum or local minimum at a point…

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

A:

Q: Find the length of the curve /- y = Vcos 2t dt from x = 0 to x = "/4.

A:

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the value of the number such that the families of curves  y =(x+c) -1  and y = a ( x+k) 1/3 are…

A: Given,

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: What is the largest vertical distance between the graphs of the functions y = Va and y x2 in the…

A:

Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

A:

Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

A:

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

A:

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

A:

Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

A:

Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

A:

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

A:

Q: 2 Find the points on the curve ax+ 2bxy + ay = c,ay = c, 0<a<b<c,whose distance from the origin is…

A:

Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

A:

Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

A:

Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

A: Minimal distance

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

A:

Q: Find the local minimum ond local moximunm Cit exists) for the funetion fex,ys = 2x? + y? + 8x -by…

A: We have to find the local maximum and local minimum of the functionf(x,y)=2x2+y2+8x-6x+20 we denote,…

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

A:

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: Find the length of the curve y Inx at (2<x< 4)?

A:

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

A:

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: What is the longest distance from the curve x ^ 2 + xy + y ^ 2 = 16 to the origin?

A:

Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

A:

Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: Find the maximum value of z=140-x+3y, under the consentrate; x≥0, y ≥0, and  2x+y ≤10, 2x+4y≤28 BE…

A:

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

A:

Q: Find the length of curve along y = x² from (0,0) into (2,4).

A:

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…