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

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168