Q/ Find the points have minimum distance from the origin to the surface хуz?-1

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

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: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: Full working plz, Thank you.

A: Suppose, I is the real image of an object O and let d be distance between the image and the…

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: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: Choose only  5-What is the maximum or minimum point for the curve y = x2 − 4 ? A) A minimum at (0,…

A: Given:- 5.  y=x2 -4  6. y = 4x-x4  To find:- Maximum or minimum value of given function

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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Q: Find the minimum distance from the parabola y=x^2 to point (0, 3)

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: Car B is b=100 miles directly east of car A and begins moving north at u=50 miles per hour. At the…

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Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: Parameterize the line of intersection of the surfaces: x2 - y2 = z - 1 and  x2 + y2 = 4

A: Given equations of surfaces are: Rewriting the second equation:

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

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Q: The equation of a curved road is given as y = 100+6x–0.015x² +0.0000111? Determine the places where…

A: The equation of the curved road given is: y=100+6x-0.015x2+0.00001111x3 Measure of the "Sharpness of…

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

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Q: Find the altitude of a rectangular close box with volume 100 with length twice the width so that the…

A: We can find the altitude of the box by using the second derivative test.

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of…

A: Given, surface, z = xy2Differentiating the z with respect to x assuming y as constant,∂z∂x = y2×1 =…

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

A: x - y2 = 0 x = y2  Let us take a point (x,y)=(y2, y) on the parabola

Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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Q: Q1 Find extrema point of the Surface 2-ペ-S-12x+3}+2

A: Consider the given function  z=x3-y3-12x+3y+12 Find partial derivatives of the function with respect…

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

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Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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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 minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.