In 1990, the population of south carolina was approximately 3,500,000. during the next ten years, the population increased by approximately 38,500 people per year. write a linear model (equation) that gives the population, p, of south carolina in terms of the year, y. let y = 0 correspond to 1990.

Step-by-step explanation:

Maybe the big numbers make it confusing, so let's look at something simpler.  If you start with 5 marbles and every day you add one marble to it how many will you have x days after startign the collection?  Well on day 0 it's 5, on day 1 it's 6, because 5+1, on day 2 it's 5+2=7, and so on.  You can write this as an equation, y = 5+x, where y is the new total and x is the number of days.  

So let's move that thinking to this problem.  1990 is day 0 and you start with 3,500,000.  Each year now instead of day you add 38,500.  So year 0 has 3,500,000.  year 1 has 3,500,000+38,500 = 3,538,500 and so on, where each year we add another 38,500.  So just like in the simpler example we can rewrite this.  y = 3,500,000 + 38,500x.  Linear means that the x is just an x instead of something like x^2, or 1/x or something else.  Just normal x.  

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.