A right helix of radius a and slope a has 4-point contact with a given 1 o' curve at the point where its curvature and torsion are a= po² p² +o² and 4/1/0 then prove that and tan a = a lo

Q: Find the equation of osculating plane at any point 't' on the helix x = a cost, y = a sin t. z = ct

A:

Q: Evaluate the arc length of the curve generated by the parametric equations below for t (-1,1) x(t)=…

A: The expression for the arc length of the parametric curve is; L=∫abx't2+y't2dt   Given: xt=3+3t2 ;…

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

A:

Q: At how many point(s) does the helix with vector equation r(t) : (cos t, sin t, t) intersect the…

A:

Q: For the curve given by r(t)=⟨−9sin(t),−1t,9cos(t)⟩, Find the curvature,

A:

Q: Find the length of the curve F(t) = (eỗ cos (‡), eỗ sin(‡), eś) for 0 ≤ t ≤ 2. Arc length =

A: To find arc length of the curve

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

A:

Q: Starting from the point (3,−4,−2) reparametrize the curve r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k in terms…

A: Given r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k Let, x=(3+1t),        y=(−4−3t),         z=(−2−3t)

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: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

A:

Q: a(0)=(r(0)cos0,r(0)sin@) Find the curvature of the curve. What are the coefficients a and b if its…

A: (a) Curvature of the curve αθ=rθcosθ, rθsinθ: Let α1θ=rθcosθα2θ=rθsinθ Then, the curve αθ is given…

Q: Which of the following statements are true (circle all that apply). (a) An arc-length…

A: We need to find the which of the given statements are true. For (a), Statement: An arc-length…

Q: на 1) A) Let V and w be vector spaces such that dim (V) = dim (W) and let T:V->w be linear. Show…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: A right helix of radius a and slope a has 4-point contact with a given curve at the point where its…

A:

Q: Consider the curve r(t) = (e' sin(2t), e' cos(2t), 2e*). (a) (b) (c) Find the osculating plane of…

A: Solution: The curve is r→t=etsin2t,etcos2t,2et

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

A: