Find the shortest and longest distance from the point (1,2, -1) to the sphere x2 + y? + z? = 24 %3D

Q: How to use the trapezoidal rule to approximate distance travel?(with a t of 1min)

A: The trapezoidal rule is used to estimate the area under a curve. The expression for the trapezoidal…

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Find the minimum distance from the point (3, 0) to the circle x2 + y2 = 4.

A:

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the minimum distance from the point (2, 4, 10) to the paraboloid given by the equation z = 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 area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

A: Given y=25-x2, 0≤x≤4 A sphere is a geometrical object that is a three-dimensional analogue to a…

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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

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Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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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: · 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: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: Find the center and radius of the sphere. * + + 5z +x+y+z= 4 5x +

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Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: The line y = mx +b intersects the parabola y = x^2 at points A and B. Find the coordinates of the…

A: The line y=mx+b intersects the parabola y=x2 at the pointsA and B.Let A=x1,x12 and B=x2,x22, where…

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

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

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: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

A:

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

A: Given surface equation is

Q: Find the least radius of curvature of the cubic parabola y=x3.

A: Given To find the radius of curvature, first find the curvature (K) using the formula. Find the…

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

A:

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

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 (2, 1, 9) to the surface x + y + z = 9.

A:

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 the radius of the sphere x^2+4x+y^2 -2y+z^2-7=0

A:

Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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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: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

Q: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

A: Here I am attaching image so that you understand each and every step.

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

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Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

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Q: Find the shortest Distance d faumthe point to the plane X+y+Z=8.

A: Let's find.

Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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

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Q: A circle with radius 1 centered at (0,) is tangent to two points of the parabola y = ². What is the…

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Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

A: