By using the calculus of variations, prove that the shortest distance between two points in the y z plane is a straight line

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D %3D x² +x – 6' has…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,…

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

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: Prove that the shortest distance between two points is along a straight line.

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Q: Find the shortest distance between the point A (3, 10) and the line y = x + 1.

A: Our Aim is to find the shortest distance between the point A(3,10) and the line y=12x+1 -(i)

Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

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Q: prove the parallelogramequlity:

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Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

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

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Q: ---2-1 N4

A: The given graph is:   Use the distance formula to find the length of the line segment.

Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

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Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a &gt; 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

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 length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: A. Find the shortest distance between the point A (3, 10) and the line y=x+1.

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Q: A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

A: Let P be the shore point Let R be the resort Let S be the point where the pipe gets the water.

Q: 51. Show that the shortest distance from the point (x1, yı) to the straight line Ax + By + C=0 is Ax…

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Q: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: Hyperbolic Geometry:        It is also a non-Euclidean geometry. It is through a point not on a…

Q: Show that the square of the length of subtangent at any point on the curve by 2 = (x+a)3,(b is not…

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Q: Determine what is the minimum distance from the origin to the line  y=-2x+5

A: topic - distance of line from origin

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 length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

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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 shortest distance from the point ( – 1, – 2, 5) to the cone z = x² + y?. Please round to…

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Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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Q: A. Find the shortest distance between the point A (3, 10) and the line y = x +1.

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Q: Prove without using the concept of duality: In the four-line geometry, there exists a pair of points…

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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: In triangular space it is sufficient to know two different points to find the line passing through…

A: Given statement is 'True'

Q: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

A: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: Determine the midpoint that lies between the two given points. (3π, 3) and (6π, 9)

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Q: (1) ( ) Find the shortest distance between two lines given x +2 -8 y = and y 2

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Q: Which is a subset of a line with one endpoint and extends infinitely in one direction?

A: A ray is a subset of a line that has only one endpoint and extends infinitely in one direction  If…

Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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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: Find a formula for the shortest distance from a point (a,b,c) to the y-axis.

A: We will find the formula as following.

Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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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: A human statue standing on a base column has a height of 4/2ft. At point P on the ground, the angle…

A: Consider the figure given below : Let 'd' represents the distance to be found out.

Q: Evaluate the length of the curve y = 3 + 3Vx +1 , 0<x< 3

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