Since
, and you have a corresponding term in the given Riemann sum of
, you know the integral is being taken over an interval of length 5, so you can omit the second choice.
Next,
corresponds to
with
. The fact that
alone tells you that the interval of integration starts at 3, and since we know the interval has length 5, that leaves the first choice as the correct answer.
Given the position function <em>s(t)</em>, you can get the acceleration function by differentiating <em>s</em> twice:
velocity = <em>s'(t)</em> = -5 sin(<em>t </em>) + 3 cos(3<em>t</em> )
acceleration = <em>s''(t)</em> = -5 cos(<em>t</em> ) - 9 sin(3<em>t</em> )
Then when <em>t</em> = <em>π</em>, the particle's acceleration is
<em>s''(π)</em> = -5 cos(<em>π</em>) - 9 sin(3<em>π</em>)
… = -5 • (-1) - 9 • 0 = 5
-1 is the opposite reciprical (perpendicular)
Quarts = 25 there are 100 in a dollar so you have 25 out of 100
25/100<span />
