Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

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Q: ind the point P on the line y = 5x that is closest to the point (78,0). What is the least distance…

A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

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Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: A line is tangent to the curve y = 3x1 and is bounded by the r- and y-axis in the first quadrant.…

A: Let's find.

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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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: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

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

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

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: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

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: 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: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

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

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Q: 1. Find the length of the curve 9x2 = 4y from (0,0) to (2V3,3) %3D

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Q: The position function of a particle is given by 7(t) = (t², 5t, t2 – 16t). When is th sneed a…

A: Given:

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 length of the curve. t,0stsV3 The length of the curve x = t°, y= ť on 0sts 3 is (Type an…

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

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Q: Use Simpson’s Rule with n  =6  to estimate the length of the curve x  =t - et -6&lt;t&lt;6

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Q: 7. Find the length of the curve y = x/4 on the interval [0,8] %3D

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Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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

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Q: 4 to Use the Trapezoidal Rule with n = 1 approximate J-1 V1-x³

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Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

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

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

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Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

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: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

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Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

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

A: Let's find.

Q: 1.) If the ball 1s Thrown vertically upward with a Veloorty of 15 m/s then ts heioht aifter t…

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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: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…