. Find sets of parametric equations and symmetric equations of the line through the point parallel to the given vector or line (if possible).

Point (-4,0,2)

Parallel to v=2i + 8j - 7k

(a) parametric equations (Enter your answers as a comma-separated list.)

(b) symmetric equations

A. 2x= y/8 = 7z

B. (x+4)/2 = y/8 = (2-z)/7

C x/2 = y = z/7

D. (x-4)/2 = y = z/7

a) Parametric equations

x = -4 + 2t

y = 8t

z = 2-7t

b) symmetric equations

         The answer is the option B

Step-by-step explanation:

For writing the vectorial equation of a line, we need a point in the line and its director vector, thus:

                            Where   is a point in the line

                                           (a,b,c) is the director vector

Then

a) Parametric equations

Since the vectorial equation, we can obtain the parametric equations writing the equation for each component

x = -4 + 2t

y = 8t

z = 2-7t

b)Symmetric equations

Since the parametric equations, we isolate the parameter t

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! )