Determine the curve whose intrinsic equations are 5.28. 1 a8 > 0, a >0 0, K 11 as +

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

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Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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Q: 1 - Findthe lenght of the Curve a) r(t)* = (3cost)i³ + (3sint)j* + 4tk¬ for 0 < t < 2n b) r(t)* =…

A: Use formula of length of curve

Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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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: メ=1 45 the right of the line , y= what is the of the unbounded regron between the grea Curve Ond the…

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Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: b) How far should we let 0 run to traverse the curves one time only?

A: To find how far θ needs to run in order to traverse the the the curve one time only, we need find…

Q: . Find the length of the curve defined by R(t) = (3t+1, 4t3/2, 4-3+2) from the point (1,0, 4) to…

A: Note : The length L of a curve r(t)→=(x(t) , y(t)  ,z(t) )  from t=a  , t=b is given by…

Q: 2 32 |for 1st<3. length of the curve c(t) =| In t,-t"

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Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: (B) The length of the curve r(t)=(1+1i+(1-nj+rV2k from the point t= to the point t=; is 2. - 112

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Q: 8 (6562) 243 를-), then xo = If the length of the curve y = 3 x7 from the point (0, 0) to the point…

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Q: Find the exact length af te of the curve, 2. x-

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Q: chuk thisynncdrs and gaph the if O-0,7 Curve r-4a Coso

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Q: 1. Consider the implicitly defined curve Py- 2r = 25. (a) Verify that the point (1,3) is on the…

A: Given,          x2y3-2x4=25

Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

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Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: Compute the length of the curve 3ti – 6tk over the interval 8 <ts 18.

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Q: Зу — 4у 3D —х — 2 The curve above can be parameterized as which of the following pairs of equations?

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Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

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Q: If U=[0 0 0 000123456777777], the number of points consisting the B-spline curve are

A: Given knot vector is, U=0 0 0 0 0 0 1 2 3 4 5 6 7 7 7 7 7 7 The knot vector is formed according to…

Q: for 4(t)- 165amun'c curve xLt)=U0st, Oco<2T, dutermine Cif any) at which the poim) cunme' has a…

A: xt=4costyt=16sint0≤t≤2π

Q: Let m be a positive real number and C be the curve given by: r(t) = m(cost – 2)ỉ – msintj + (mt –…

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Q: 10.Show that Φ(t) = Ψ(t)Ψ−1(t0), where Φ(t) and Ψ(t) are as defined in this section.

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Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

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Q: Let m be a positive real number and C be the curve given by: r(t) = mcosti – m(sint + 3)j + (5 –…

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Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval…

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

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: Consider the path r(t) = (12t, 6t², 6 ln t) defined for t > 0.

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Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: 5. dr, wher 2 C is curve x

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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: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

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Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: 7 Find the stationary point on the curve e + ye = 2e'. %3D

A: In the given question, the concept of the stationary point is applied. Stationary Point The critical…

Q: 1- Fit a least-square geometric curve y = ax to the following data 2 3 4 5 y 27.8 62.1 110 161

A: We have to find Geometric Curve using least square method.