The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.
To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.
By definition of absolute value,
Over this particular integration interval,
• sin(<em>t</em> ) ≥ 0 for 1 ≤ <em>t</em> < <em>π</em>, and
• sin(<em>t</em> ) < 0 for <em>π</em> < <em>t</em> ≤ 5
so you end up splitting the integral at <em>t</em> = <em>π</em> as
Now compute the distance:
making B the correct answer.
The answer is yes. all 3 of those triangles have perfect square roots, being 5, 12, and 13 respectively. I hope this helps! Could I possibly get brainliest?
Answer:
Step-by-step explanation:
you have a 29 of 38 chance at lossing
When 
, we have
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for 
, that
Now for 
, we have
so we know the left side is at least divisible by 
by our assumption.
It remains to show that
which is easily done with Fermat's little theorem. It says
where 
is prime and 
is any integer. Then for any positive integer 
,
Furthermore,
which goes all the way down to
So, we find that
QED
