Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s= V(T) dt. Then find the length of the indicated portion of the curve. r(t) = (4 + 5t)i + (8 + 2t)j + (2 - 7t)k, -1sts

L = 8.831 t

Step-by-step explanation:

You have the following vector:

To find the arc length you use the following formula:

  (1)

where dx/dt, dy/dt and dz/dt are the components of the vector dr/dt.

Then, you calculate dr/dt:

Next you replace in the integral of the equation (1):

hence, the arc length is L = 8.831t

people went from manufacturing one object at a time by hand to manufacturing many objects in factories

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: