Thread: 3 ?'s that i need help on!!

1. 3 ?'s that i need help on!!

questions on attachment!!

2. Question #3]
$\displaystyle {5 \choose 2}=\frac{5\cdot 4}{2!}=10$

3. Hello, Lane!

1. The polulation of a city in 1991 was 350,986.
The population of the same city in 1996 was 523,026.
Assuming that the change in the number of people is constant over five-yer periods,
find a formula for the population of the city $\displaystyle n$ five-year periods after 1991
and predict the population of the city in 2016.

I hope you aren't asking, "What the formula?"
. . You can baby-talk your way through it.

In the five years from 1991 to 1996, the population grew: $\displaystyle 523,026 - 350,987 \,=\,172,039$

Assuming that this rate of change of the population is constant,
. . the population will increase by 172,039 people every five years.

Therefore, in $\displaystyle n$ five-year periods after 1991, the population will be:

. . $\displaystyle \boxed{P \:= \:350,987 + 172,039n}$

In 2016 (25 years later, or 5 five-year periods later), the population will be:

. . $\displaystyle P \:=\:350,987 + 172,039(5) \:=\:\boxed{861,532}$

2. Use the binomial theorem to expand and simplify: $\displaystyle (s - u)^5$

What part of "binomial theorem" don't you understand?

$\displaystyle (s - u)^5\;=\;\binom{5}{5}s^5 + \binom{5}{4}s^4(-u )+ \binom{5}{3}s^3(-u)^2 +$$\displaystyle \binom{5}{2}s^2(-u)^3 + \binom{5}{1}s(-u)^4 + \binom{5}{0}(-u)^5$

. . . . . . $\displaystyle =\;\boxed{s^5 - 5s^4u + 10s^3u^2 - 10s^2u^3 + 5su^4 - u^5}$