Question

In: Advanced Math

Given the curve −→r (t) = <sin3 (t), cos3 (t),sin2 (t)> for 0 ≤ t ≤...

Given the curve −→r (t) = <sin3 (t), cos3 (t),sin2 (t)> for 0 ≤ t ≤ π/2 find the unit tangent vector, unit normal vector, and the curvature.

Solutions

Expert Solution

The tangent vector anf unit normal vector and curvature are calculated with standard formulas specified

The final answer is too lengthy..hope you understand.


Related Solutions

The arclength of the curve r(t) = 2 cos3 (πt/2), 2 sin3 (πt/2), 1, between the...
The arclength of the curve r(t) = 2 cos3 (πt/2), 2 sin3 (πt/2), 1, between the points r = (2, 0, 1) and r = (0, 2, 1), is given by?
The curve C is given by the parameterization ⃗r(t) = <−t , 1 − t^2> for...
The curve C is given by the parameterization ⃗r(t) = <−t , 1 − t^2> for −1 ≤ t ≤ 1. a) Choose any vector field F⃗ (x, y) = 〈some function , some other function〉 and setup the work integral of F⃗ over C. b)Choose any vector field G⃗(x,y) which has a potential function of the form φ(x,y)= x^3 + y^3 + some other stuff and compute the work done by G⃗ over C. Please use a somewhat basic...
Find T(t), N(t), aT, and aN at the given time t for the space curve r(t)....
Find T(t), N(t), aT, and aN at the given time t for the space curve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in the equation a(t)=aTT+aNN. (If an answer is undefined, enter UNDEFINED.) Function    Time r(t)=9ti-tj+(t^2)k t=-1 T(-1)= N(-1)= aT= aN=
Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show...
Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show the following: Show T3⊆Span(F3). Show F3⊆Span(T3).
2. Consider the plane curve r(t) = <2cos(t),3sin(t)>. Parameterize the osculating circle at t=0. Sketch both...
2. Consider the plane curve r(t) = <2cos(t),3sin(t)>. Parameterize the osculating circle at t=0. Sketch both the curve and the osculating circle
Solve the given equation. 7 sin2(θ) − 36 sin(θ) + 5 = 0
Solve the given equation. 7 sin2(θ) − 36 sin(θ) + 5 = 0
solve the given equation. 7 sin2(θ) − 22 sin(θ) + 3 = 0
solve the given equation. 7 sin2(θ) − 22 sin(θ) + 3 = 0
(1 point) If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial...
(1 point) If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a particle moving along C.
Calculate the arc length of the indicated portion of the curve r(t). r(t) = i +...
Calculate the arc length of the indicated portion of the curve r(t). r(t) = i + (9t sin t)j + (9t cos t)k ; -3 ≤ t ≤ 7
Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1...
Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1 – R[t]/K) - sR[t]W[t] W[t+1] = (1-u)W[t] + vR[t]W[t] Where the carrying capacity of rabbits is 1 million. The growth rate of rabbits is 10% a year and s is equal to 0.00001, v is 0.0000001, and u is equal to 0.01. How many wolves and how many rabbits exist in the equilibrium?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT