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Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. r(t) = (4t^2,8t^2, root 89t^2), for 1 leq t leq 4 r(t) does not use arc length as a parameter. A description of the curve that uses arc length as a parameter is r(s) = (Type exact answers, using radicals as needed.)

Respuesta :

adioabiola

The curve does not use an arc length as a parameter

If |v(t)| = 1, for all t ≥ a, then the parameter t corresponds to arc length.

|v| = |r'| × |v| =√4t² + 16t² + 64t²

=√84t

=2√21

It is not equal to 1, so it doesn't use arc length as a parameter.

Also,

s = √21t

r(s) =(s/√21, 2s/√21, 4s/√21)

for

√21 ≤ s ≤ 16√21

|r'(s)| = (1/√21) × √1+4+16

= 1

What is arc length?

This is the length of a segment of an arc

In order words, an arc length is a fraction of the circumference of the circle

Learn more about arc length:

https://brainly.com/question/2005046

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