A fireplace arch is to be constructed in form of a semiellipse. The opening is to have a height of 2 feet at the center and a width of 6 feet along the base. The contractor cuts a string of a certain length and nails each end of the string along the base in order to sketch the outline of the semiellipse. 1. What is the total length of the string?

2. How far from the center should the string be nailed into the base?

The total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Step-by-step explanation:

Circumference of ellipse =

Circumference of semi-ellipse =

we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.

So,

Circumference of semi-ellipse =

Distance from center =

Hence the total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

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! )

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.