Find the minimum distance from the origin (0,0,0) the line L: 1 +t -3 distance =

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: 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 the minimum distance from the point P with coordinates (1. 2. 1) to the line r = a+Ab, where a…

A: The minimum distance from the point P(1,2,1) to the line r is the perpendicular distance between P…

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 length of the curve. 33 X = x=11t°, y= ², t,0stsv3

A:

Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

A:

Q: Find the length of the curve y =x/2 from x = 0 to x = 3.

A:

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

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 to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

A:

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: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

A:

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

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

A:

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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: Given y=[cube rt]x, find the local linear approximation for y near x=-8 and use it to estimate the…

A: Given: The function y=x3 To find: The local linear approximation for y near x=-8 and using this…

Q: Let L be the line with equation y = x – 1. Find the minimum distance between L and the point (4, 5)…

A: In order to use method of Lagrange multiplier, we first need to find the function to be minimized.…

Q: Find the length of the curve y=x^3/2 from the point (1,1) to the point (4,8).

A:

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

A:

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 length of the curve y = 1 - e^-x, 0 &lt;=x&lt;=1.

A: The given curve is

Q: Find the length of the curve y = x/2 from x =| 0 to x = 3.

A: We have to find out the length of curve.

Q: ) Prove that the Point P(!,-) is a minimum Point of the curve y =lnx

A: Any point (x,y) is minimum for a given curve if it satisfies below two condition, a) First…

Q: Find the are length of the curve x = (y² + 2)/2 from y-0 to y=1

A: First, calculate dxdy for the equation, x=13(y2+2)32  . Then, use the formula, L=∫ab1+dxdy2 dy to…

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

A:

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

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

A:

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

A:

Q: Find the are bounded by the curve y=x²-4, the lines y=0 and x=4.

A:

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

A:

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: Find the length of the curve. y = In(secx), 0Sx</4

A:

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

A:

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

A:

Q: find the distance from the point to the line (2, 2, 0); x = -t, y = t, z = -1 + t

A: Given information: The point to the line is (2, 2, 0) and x = -t, y = t, z = -1 + t. Calculation:…

Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

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

A:

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. *

A:

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 y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

A:

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

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.