By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1 and u = y2, find the minimum distance in the xy-plane from the line y = x + 1 to the pa-rabola y2 = x.

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: We cannot plot the 4D graph (x, y, z, w) of a function of three variables w = f(x, y, z), but we can…

A: As per the question we are given the following trivatiate equation : w = x + z2 And we have to…

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

Q: The differential equation: y' (t) − y(t) = 0 can be written in a vector equation: ´y' (t) 1 'y' (t)…

A: False

Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: Use the method of Lagrange multipliers to find the minimum and maximum values of the function f (x,…

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Q: Linear Functions Problem Solving Task Heidi and her family want to know if Cable is the best choice.…

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Q: Find the shortest distance between the line L1:2x + y - 3 = 0 and the plane P1:3x - 4y + 12z + 5 =…

A: The formula for the distance between a point and a plane must be used to determine the shortest…

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Consider the function f(x, y) = x ^3 + y ^3 + 3xy and the constraint (x − 3)^2 + (y − 3)^2 = 9.…

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Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: Find the point where the function f(r, y) = r² + 4y² + 12 subject to the constraint z + y = 5 takes…

A: f=x2+4y2+12..............(1) the given constraint is  x+y=5 y=5-x................put it back in…

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

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Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

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Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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Q: Find the minimum value of f(x, y, z) = 3x² + y² + 3z² when the domain is constrained to the planes…

A: f(x,y,z)=3x2+y2+3z2subject to the given constraints−4x+y+3z=−4−2x−y+5z=−3 Set up the…