Find all points on the surface x2 + y2-22 1 at which the normal line is parallel to the line through P(1,-2. 1) and Q(4, 0,-1). %3D

Q: Find the orthogonal trajectories of the family of curves y=Ce* +10

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Q: Find the average value of f(x,y)=3xy over the rectangle R with vertices (−1,−2),(1,−2),(−1,0), and…

A: We have given f(x,y)=3xy Rectangle R with vertices (−1,−2),(1,−2),(−1,0), and (1,0).

Q: 3. Find the equations of normal of the curve y = 2x- x-at (2, 0). Oa. 2x +y = 4 b. 2x - y = 2 C. X-…

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Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 19, (1,…

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Q: What is the equation of the normal line to the curve x2 + y? – 6x - 2y=0 at (2,4)? A x+3y- 10 = 0 B)…

A: We need to find equation of normal line.

Q: Given the curve y = x´ and the line y =2- x Find the ordinate of the centroid of the region bounded…

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Q: Find the normal lies to the curve ru + 2x – u = 0

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Q: Find the equation of the normal line of y = 8 – x³ at (-1 , -3) а. 8-Зу — х %3D 0 b. х— Зу — 8 %3D 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: need help evaluating this quesion pls

A: Consider the given information:

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Q: Find the coefficients a,b in the function f(x)=ax+b so that (f(x1)-y1)^2+(f(x2)-y2)^2+(f(x3)-y3)^2…

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Q: In Exercises 36–38, find the point on the given curve closest tothe specified point. Recall that if…

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Q: The data below obtained from the experiment: 3.6 f (x)| 0.7555 | 0.6206 | 0.5052 0.4812 | 0.4498…

A: Given that, The data obtained from an experiment is as shown below. x 1.5 1.8 2.4 2.7 3.2 3.6…

Q: Find the normal line for the level surface f(x,y,z) = 7x³ + cos (4y) + In (4z) = c at the point…

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Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

Q: Find the equation of the normal line to the graph y= x In x that is perpendicular to the line x - y…

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Q: Find the maximum value of f(x, y) = 11zy(9 – 99x – 9y) over the triangle with vertices (0, 0). (†,0)…

A: Given: The triangle vertices are (0,0),(111,0) and (0,1) f(x,y)=11xy(9-99x-9y)…

Q: Find the equation of the normal line in the symmetric form at the point (10, 10, 10) to the surface…

A: Given:     Equation to the surface is 3x4+3y4+6z4=12…

Q: 48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point…

A: Given that: f(x, y, z)=xyz+3

Q: 11. What is the symmetric equation of the normal line to the ellipsoid x? + 2y? + 32 = 6 at P(1,1,…

A: solution:  Given  ellipsoid⇒x2+2y2+3z2=6at point(1,1,1)let f(x,y,z)=x2+2y2+3z2-6

Q: The equation of the normal line to the curve y = -Vx that is parallel to -6x +y = 1 (A) y + 3 = –6(x…

A: equation of curve y=-x equation of line -6x+y=1

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

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Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Given ellipse with centers at (0,0) and two vertices (1,0) and (-1,0).

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

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Q: 2. At time t sec, the positions of two particles A andB on a horizontal coordinate line are sA = 3t3…

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Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 2²-2y²-3²= -4…

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Q: ve the least square equations for fitting a curve of the type b y = a x² + - - set of n points.…

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Q: The equation of the normal line to the curve y = -Va that is parallel to -6x+y = 1 (A) y + 3 =…

A: given,     curve y=-x is parallel to -6x+y=1

Q: 1. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1).

A: Please see the below picture for detailed solution.

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: Let F(x,y,z)= (6ye?,2e?,12(2-e?)). Let S be the portion of the graph z=In(6x2+120y3+2) which is…

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Q: Find the equation of the normal line to the curve y = x³+ 3. at (1, 4). %3D O a. x = 1 O b.y = 4 O…

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Q: Determine a region of the xy-plane for which the given differentail equation would have a unique…

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Q: Q3A)Find normal line and parallel plane to the function f(x, y, z)=√xyz - 4 At point (1,2,8).

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Q: Picture attached. Thanks in advance!

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Q: 3. Find the extreme values of the given f(x, y) on the indicated surface. f (x, y) = 8x² – 2y; x² +…

A: The solution of the problem is given in the next step.

Q: 18. Find the equations of the normal lines to the curve y = x3 - 4x that is parallel to the line x…

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Q: Determine the position of the y-centroid of the line from x = 1 to x = 5.

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Q: Find the linearization L(z, y) of f at the given point. Surface: f(a, y) In(x +9y) Point: (11e5,e)…

A: Given :

Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

Q: Let F(x,y,z)=(2ye?,2e²,12(2-e?)). Let S be the portion of the graph z=1n(2x2+40y3+2) which is above…

A: Given that: Fx,y,z=2yez,2ez,122−ez Here S is the portion of the below graph which is above the given…

Q: Let F(x,y,z)= (4ye?,2e?,12(2-e?)). Let S be the portion of the graph z= In(4x2+60y3+2) which is…

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Q: onsider the DE vy" – y' + y = 0. ) Is this DE linear? ) If it is linear, is it omogeneous?

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: Consider a function: fx, y, z=tan-1xyz……1   Given point, say A, is: A=1, 1, 1   On comparing A with…

Q: Find the absolute maximum and minimum values of f(x, y) Зху — Зх — бу + 9 %3D | on the closed…

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Q: Which of the following give the symmetric equations of the normal line to the surface xy + yz + zx =…

A: Normal to the surface is a line perpendicular to that surface.