J.89 he tangential and. accelntion of a pakticle moving gloen by Show that nomal on CUrue space and k(ds/dt)) where the the dec lengith from Gome is the chC of initial paint and Curve measured 60me is. the cuouatule.

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A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

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Q: Determine the length of the tangent to the circle x? + y? - 4x - 5 = 0 from (8, -2). * 2.89 5.57…

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Q: Find the equation of the tangent plane to the surface z = cos(8x) cos(y) at the point (−2π/2, 3/2,…

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Q: Find the angle between the curves y = x² and y = x³ at their point of intersection. Select one: O a.…

A: y=x2 y=x3 The point of intersection can be calculated as shown below; x2=x3 So, x=1

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Q: = (b) The elastic cylinders are brought into contact at an angle a = 45° angle. The cylinders are…

A: Given: a=45° R1'=R2'=0.05m R1''=R2''=∞ To find: In the given derivation how the term cos2a become…

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Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: 4. The position of a particle at time t is given by x(t) = 5+4 sin(t) y(t) = 2 − 4 cos(t) 0<t</ (a)…

A: This is a problem of parametric curve and Integration.

Q: a) Find the length of the curve: y = [1,2].

A: Given curve is y=x416+12x2on the interval [a, b]=[1,2]y'=dydx=x34-1x3

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Q: Show that tan²t+ cot2 t = 1 is a a² possible form of the boundary sur face o aliquid and find an ex…

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Q: find work done Let F = ) and let c be unit circle centered on(2,0) note:r? not constant

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Q: ply) = secly) + e ² Find p'ly)

A: Solve for the derivative

Q: (ii) Prove the following Frenet-Serret formulae: T = KUN, N-KUT+TU B.

A: