Answer! 6. Compute yz dz + zzdy+ zydz along the curve (cos t, sin t, tan t). 0sts*

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

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Q: 4. Evaluate 2.x cos y dx – x sin y dy along the elliptical path + y? = 1 from (2,0) to (0, 1)…

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Q: Consider the helix r(t) = (cos(4t), sin(4t), –2t). Compute, at t

A: Compute unit binormal and curvature at t=pi/6

Q: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

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Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

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Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIS#/2.

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Q: 2. Write an arc length parameterization for the curve r(t) = cos ti + sin tj + 3t k ; 0<t

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Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

Q: Find the length of arc of the given curve. 5. R= (sin 2t , cos 2t , 2t³/2), 0 sts1.

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Q: 3) Find the length of the curve r= cos (0/3), 0< 0 <"/4:

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Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: Let C be the curve defined by T(t) = (2 + 2 sin(t), 3 – 2 cos(t)) for 0 < t < 4x=²) dx + (2xyev" +…

A: Given the integral is ∫Cy2exy2+4x-2dx+2xyexy2+2dy. Rewrite the integral as ∫CF·→dr→:…

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

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Q: Find the length of the curve x = cos t, y= sin t, 0 <IST. 4/2 4 IT 2/2 IT 2 2

A: Given that: x=cos2t, y=sin2t, 0≤t≤π

Q: 1. Evaluate xyz dz, where C is the curve 7(t) =t cos(t)î + sin(t)ĵ – cos(t)k, 0 < t <1.

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Q: Consider a particle moving along a path C given by r(t) = v3ti+ = V3ti sin (t)j + cos (t)k Find the…

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Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

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Q: Prove that the curve r(t) = (a cos t,b sin t,.csint is parameterized by length provided a=b2 +c² =…

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Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: What is the length of the curve x = cos t + t sin t, y = sin t – t cos t, (0 < t < 2x) ? Lütfen…

A: First I have written the Arclength formula for the parametric curve , then using that formula and…

Q: Let C be the curve.

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Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

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Q: Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: Compute the arc length of the indicated portion of the curve: 7(1) = (7 +2r²)î + (21² – 4)ĵ + (7 –…

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Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -5 sts 5

A: To determine the length of the curve.

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: 5. R = (sin 2t , cos 2t , 2t3/2), 0 <t<1.

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3In(cos(t)) k, 0 stsn/4 Submit Answer

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Q: The arc length of the curve r= cos 30 with 0<0 < is T V(sin 30)² + (cos 30)² do 0. o" V-9(sin 30)² +…

A: Given that: r=cos3θand  0≤θ≤π

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

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Q: Find the length of arc of the given curve. 5. R= (sin 2t, cos 2t , 2t³/2), 0 sts1.

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Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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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: 2.2 Prove that e zp- 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: Prove that e dz < ++1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

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Q: What is the area of one of the petals of the rose curve r = 2 cos(20)? T/4 cos (20) d0 8. cos (20)…

A: We have to find

Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3

A: For the curve r(t) = f(t) , g(t), h(t)On the interval [a, b]The length is given by L =…

Q: 26. Inside the lemniscate r² = 6 cos 20 and outside the circle r = v3 V3 %3D

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Q: " | and F(x.y) = <y-x, x+3), then TE If C is the curve parametrized by 7(1)= <2sint, 2cost), te 0,-…

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Q: *:VP+o* dt =+ o? + n(* + vP + o*). (Round your answer to one decima Compute the length of the curve…

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Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.