Question

Need help on the blanks. Pretty lost atm

Answer 1

Answer:

• -108.26
• -108.13
• -108.052
• -108.026
• -108

Step-by-step explanation:

A graphing calculator or spreadsheet is useful for making the repeated function evaluations required.

The average velocity on the interval [a,b] will be ...

  v avg = (y(b) - y(a))/(b-a)

Here, all the intervals start at a=3, so the average velocity for the given values of t will be ...

  v avg = (y(3+t) -y(3))/((3+t) -3) = (y(3+t) -y(3))/t

This can be computed for each of the t-values given. The results are shown in the attached table.

__

We note that the fractional part of the velocity gets smaller in proportion to t getting smaller. We expect it to go to 0 when t goes to 0.

The estimated instantaneous velocity is -108 ft/s.

_____

We can simplify the average velocity equation to ...

  v avg = ((48(3+t) -26(t+3)^2) -(48(t+3) -26(3)^2)) / t

  = (48t -26(t^2 +6t))/t

  = 48 -26t -156

  v avg = -108 -26t

Then the average velocity at t=0 is -108.