7. Consider the Helix: r(t) = (R cost, R sint, Rt), 0 ≤ t ≤ 2π for R a constant. A. Calculate the work in the presence of F = (-y, x,-z) when moving a particle along r(t) from t = 0 to t = 2π. B. Calculate the mass of a wire in the shape of the helix r(t) from t = 0 to t = π with density 8(x, y, z) = x + y.

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: The wavefunction of a mechanical wave on a string is described by: y(x,t) =…

A: The velocity function is calculated by differentiating the displacement function with respect to t…

Q: 2. Find parametric equations for the line that is tangent to the curve 7(t) = (cos(t), et,4 – 3t) at…

A: Solution:-

Q: Evaluate I = f (z, x, y). dr and C is the helix of r(t) = (cost, sin t, 3t) sketch the curve C.

A: Given,               I=∫Cz, x, y·dr, and C is the helix of r(t)=cost, sint, 3t.

Q: Q1:- Find T(t) and N(t) for the curve helix x = a cos t, y = a sint and z = ct, and then find B(t),…

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Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

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Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: For the curve r(t), write the acceleration in the form a+T+aNN. r(t) = (6t sin t+ 6 cos t)i + (6t…

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Q: The helix r,(t)= (1+cost,- sint,t) intersects the curve (2,0,0). Find the angle of intersection. i,…

A: Given,           Both intersects each other at the point (2, 0, 0). We have to find the angle of…

Q: Find the equation of the osculating plane of the helix: r(t) = sin(3t), y(t) = 2t, 2(t) = cos(3t)…

A: Given the equation of the helix:     x(t)=sin(3t), y(t)=2t, z(t)=cos(3t) So, rt=sin3t,2t,cos3t. Find…

Q: Complex space and hoke Hl 20J. define the operator Te=(xh)k i when T Self Let H be Hilbert we To H→H…

A: Given that the operator T is defined as T:H→H by Tx=x,hk where h,k are fixed. For every operator T…

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: The path r(t) = (t- sin t) i+ (1- cos t) j describes motion on the cycloid x=t- sin t, y=1- cos t.…

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Q: The helix  r(t) =   cos(πt/2), sin(πt/2), t    intersects the sphere  x2 + y2 + z2 = 2  in two…

A: Given helix r(t)=cosπt/2, sinπt/2, t intersect the sphere x2+y2+z2=2             in two points.

Q: Find arclength s(t),curvature k(t) and the unit tangent vector T(t)f or…

A: Find arclength s(t),curvature k(t) and the unit tangent vector T(t)f or…

Q: A sheet of water of uniform thickness (h= 0.03 m) flows from the device shown in the figure below.…

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Q: 2 Find the curvature and the vectors T(t), N(t), B(t) for (t)=(√2 cost, sint, sint) at the point the…

A: We need to find curvature and vectors.