Answer :
By The length of the curve can be found using the formula for the arc length of a parametric curve, the distance traveled by the particle is 30π.
The length of the curve can be found using the formula for the arc length of a parametric curve:
L = ∫0→5p √(dx/dt)2 + (dy/dt)2 dt
We can calculate dx/dt and dy/dt as follows:
dx/dt = 6sin(t)cos(t)
dy/dt = -6sin(t)cos(t)
Substituting these values into the formula for the arc length gives us:
L = ∫0→5p √[(6sin(t)cos(t))2 + (-6sin(t)cos(t))2] dt
= ∫0→5p 6√(sin2(t)cos2(t)) dt
= 6∫0→5p |sin(t)cos(t)| dt
= 6∫0→5p sin(t)cos(t) dt
= 6[(1/2)sin2(t) + (1/2)cos2(t)]5p
= 6[(1/2)(1) + (1/2)(1)]5p
= 6(1)5p
= 30π
Therefore, the distance traveled by the particle is 30π.
Learn more about distance here
https://brainly.com/question/28956738
#SPJ4
