Investigation Consider the helix represented by the vector-valued function r(t)= < 2 cos t, 2 sin t, t > (a) Write the length of the arc son the helix as a function of t by evaluating the integral s= int_{0}^{t} sqrt{[x'(u)]^{2} + [y'(u)]^{2} + [z'(u)]^{2} du}

emancipezN 2021-01-08 Answered
Investigation Consider the helix represented by the vector-valued functionr(t)= < 2 cos t, 2 sin t, t >(a) Write the length of the arc son the helix as a function of t by evaluating the integrals= 0t [x(u)]2 + [y(u)]2 + [z(u)]2 du
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

crocolylec
Answered 2021-01-09 Author has 100 answers
To calculate: The length of the arc s on the helix as a function of tThe length of the curve is s= 5t.Used formula: s= 0t [x(t)]2 + [y(t)]2 + [z(t)]2 dtCalculation:The helix path is,r(t)= < 2 cos t, 2 sin t, t >On differentiating this vector value function,r(t)= < 2 sin t, 2 cos t, 1 >Calculate the length of the line segment for the given interval ass= 0t [x(t)]2 + [y(t)]2 + [z(t)]2 dt
= 0t (2 sin t)2 + (2 cos t)2 + (1)2 dt
= 0t 5dt
=5tThus, the arc length is s=5t.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-11
Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).
asked 2022-07-27
Polar coordinates of a point are given. Find therectangular coordinates of the point. ( 3 , 135 )
asked 2022-04-14
Find semi-major/semi-minor axis of ellipse from parametric equations with different phase
x=x^cos(Ωtθ)
y=y^sin(Ωtφ)
asked 2022-06-01
Calculate   d x 1 + x 4   x   sin [ n π ϕ ( x ) ]   ; ϕ ( x ) 0 x d y 1 + y 4
asked 2021-11-06

The following are each a result of a single transformation. What type of transformation occurred for image F'.
PreImageImageA(3,4)A(4,5)B(5,10)B(15,30)C(2,3)C(2,3)D(3,7)D(7,3)E(2,6)E(5,0)F(5,9)F(5,9)

asked 2022-06-14
I am attempting to use Euler's method to express the following system of ODE's...
d y i d x = c i ( y i 1 3 y i 3 ) + f i ( for  i = 1 , , n )
using the discretised equations, which are presented below in matrix notation:
y ( t k + 1 ) = C 1 y ( t k ) + C 2 y 3 ( t k ) + f
Note f i = 1 when i = 1, but otherwise equals 0 (this considers the initial condition). Whilst I am familiar with Euler's method, I am unsure of the steps to get to the first equation to the second. Can anyone assist me with this? Understanding this is necessary for a project I'm working on, so I would really appreciate any help.
asked 2021-04-11
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
9x2+64

New questions