Use the Least-Square method to find a line in the form of a= do – d · I that best fits the following 3 points: (1, 0), (–1, 2), (3, 4)

Q: Find the distance between the following skew lines -y+14, z= X-1 y =z+3 2 2

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Q: Find the equations of the normal line to the surface z = 8x°y" at the point (– 2, – 1,64). y = z = -…

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Q: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Find the parameters c,,c, of the line y=c,+c,x that gives the best-fit (in a least-squares sense) to…

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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: Find the point at which the line f(z)= 5z + 21 intersects the line g(z) = - 2z -7 %3D -2 11 Submit…

A: To find the intersection point of the lines f(x)=5x+21 and g(x)=-2x-7.

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find two nonnegative numbers x and y such that xy 56 and 7x + 2y is minimized. y =

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Q: Find whether the planes below intersect, and if so, where they intersect using Gaussian elimination.…

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Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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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: The points P= (x, x, x) and Q (y,3y.y-1) are lines in R' that do not meet. Choose x, y to %3D…

A: Given that P=x,x,x  and Q=y,3y,y-1 Then    P-Q=x,x,x-y,3y,y-1⇒P-Q=x-y,x-3y,x-y+1 then, we solving…

Q: Find the distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

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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: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Given:  The equation of cone is z2=x2+y2. To determine: The points on the given cone that are…

Q: 3. For the lines L;:x = 4t – 1, y=t- 3, z=1 and L2: x= 12t + 11, y=1+ 6t, z= 2 + 3t a. Show that the…

A: Answer

Q: Use Lagrange multipliers to find the point whose coordinates are all positive at which the function…

A: To find - Use Lagrange multipliers to find the point whose coordinates are all positive at which the…

Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find the least squares straight line y = mx+b to fit the data points: (1,3), (2,2), (3, 4). Compute…

A: The equation of least square straight line y=mx+b can be found by calculating m and b from the given…

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5", where the value ab is as…

A: We need to find the minimum value of ab So, let fx,y=xy We need to minimize this function and find…

Q: Find the absolute maxima and minima of f(x, y) = 3x2 + 10y on the closed triangular region bounded…

A: Consider the equation

Q: Use Lagrange multipliers to find the point on the plane  x − 2y + 3z = 6  that is closest to the…

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Q: Find the Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: Find the equation of the normal line to the parabola y = x + 3x – 2, that is also parallel to 7x…

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Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: 3) Let r1(t) = and_r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

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Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: Use Lagrange multipliers to find the highest and the lowest points on the curve of intersection of…

A: Here we have to find the maximum and minimum value of z=x2+4y2 subject to constraint x2+y2=1.

Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

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 equations of the normal line to the surface z = 2a'y* at the point (2, – 1, 16). | x = y =…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let the point on the cone is P(x,y,z). The the distance of the point P from the given point…

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: Find the distance between the skew lines defined by L1:(t) = L2: r2(s) =

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Q: Use the method of Lagrange multipliers to find the points on the circle x2 + y2 = 52 that are…

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Q: Use the Least - Square method to find a quadratic function of the f(t) =xo + xt +xzt? that best fits…

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