Evaluate S.(x – 3y² + z) ds for each of the following curves.

Q: 1. Consider the family of curves 1 y = Vx +C Find its domain. Find the specific member of orthogonal…

A: first we will find the domain of the given function then we will find the differential equation…

Q: 42. Find the family of curves that is orthogonal to the fam- ily defined by the equation y? = cx and…

A: 42. given curve is                                           derivative of the curve is…

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: How do I do this?

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Q: Let C be the curve y = 2.5 In (6.25 – x²), for – 1.2 < x < 1.6. A graph of y follows. 4.6 4.5 4.4…

A: Here, y=2.5 ln6.25-x2. So,         y'=2.5ln6.25-x2'           =16.25-x26.25-x2'    =2.5·16.25-x2-2x…

Q: Let C1 be the oriented plane curve given by the graph of y = sqrt(x) from (0,0) to (4,2) let C2 be…

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Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t&gt;0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

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Q: 1. Find the are length of the curve x (+ 2)/2 from y=0 to y-1

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Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Which of the following is the orthogonal trajectory of the family of 8. curves cz? + y? = 1?

A: Given: The given curve is cx2+y2=1

Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

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Q: 1) Evaluate S,(x – y)dx + (y – z)dy + xdz where C is the curve from (1. –2, 3) to (–4, 5, 2) if a) C…

A: Given integral: ∫Cx-ydx+y-zdy+xdz Here, C is the curve from 1,-2,3 to -4,5,2 a) The parametric…

Q: 6a. Find . F dr, where F(x, y) = , and C consists of the circle x' + y = 4 from (2,0) to (v2, v2)…

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Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: y = 4 1 ,2 In x, 1<x < 2 2 -

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Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: Straight lines with slope twice the x-intercept.

A: Let us assume x-intercept is a. That is, x = a when y  =0. So,  slope  =2a. Let us assume that the…

Q: Find the length of the following three-dimensional curve r(t) = (1+ 3t,4 - 3t, – 6 + 2t) , for 1sts7

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Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

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Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

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Q: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: In Pi Jinxing's dream, two curves are said to be CoRoNaViRaL if whenever they intersect, the two…

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Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

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Q: Let C be the curve starting at -3,3) and going along a straight line to 3,-3) and then…

A: We will use basic knowledge of line integral and curve parametrization to solve this question

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

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: we find the intersects of yab and yed with the x and y axes: Pe (0, Yable-=o) = (0, 5) 3 (0,…

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Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

A: Given that, There is a circle which center is at origin anf the radius is R. x = 10, y = 20 We have…

Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: 1 ,3/2 y92 - y"2 between the points 3 ,1 and (6,9). 3 Find the length of the curve x=-y" 1/2

A: Given : The curve is : x=13y32-y12  We have to find the length of the given curve between the points…

Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

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Q: Evaluate S,(x – 3y² + z) ds for each of the following curves. |

A: We have to find the line integral.