Let $f(x)$ be a twice differentiable function over $[a, b]$ with arc length $l$. show that there exists a value $c \in [a, b]$ such that the angle $\theta$ between the tangent line and the horizontal line at $x = c$ satisfies $|\cos\theta| = \frac{b-a}{l}.$

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

0.02040816326

c) yes, because of asa or aas