Question

Question Attached

Answer 1

I believe it is 1200 because all you have to do is read the graph :)

Answer 2

R is the amount of people joining the line, so I need to find the integral from 0 to 5 of the whole graph

Answer 3

But I do not know exactly how to find the integral- do you know how?

Answer 4

no, I don't I' sorry. Good luck!

Answer 5

Since the function is piece wise, you'll need to integrate each part separately.

Answer 6

We will let \(t\) be in hours, and say noon is hour \(0\).

Answer 7

We'll find the number of people to show up by 2 P.M

Answer 8

\(p\) will the function for the number of people at any time.

Answer 9

\[
p(2)-p(0) = \int_0^2 R(t)~dt
\]Between noon and 2 P.M. we have \(R(t) = \frac{2100-800}{2-0}t+800\).
I used the slope point formula to get this.

Answer 10

Keep in mind they already tell us \(p(0) = 300\).

Answer 11

ah okay so then it would be the integral from 0 to 2 of 650t+800

Answer 12

Whoops, I should have put \(\frac{1200-800}{2-0}\).
Do you understand how I got that?

Answer 13

Ah yes using the formula y=mx+b

Answer 14

Okay, so you should be able to get the other \(R\) functions for other intervals.

Answer 15

so then it would be integral of 0 to 2 from 200t+800

Answer 16

and then the next integral would be from 2 to 3 of (1200-800) t + 1200 Am I correct?

Answer 17

no it would be (800-1200)t +1200

Answer 18

integral from 2 to 3 of (-400) t + 1200 right?

Answer 19

The intercept is not going to be \(1200\). before it was a special case that the intercept and initial point were the same.

Answer 20

Wait so how would I go about finding the intercept?

Answer 21

Well, we start with \(y=mx+b\).

Answer 22

We have the equations: \[
y_2=mx_2+b \\ y_1=mx_1+b
\]Two linear equations, two variables.

Answer 23

Basically, when you have \(m\), you can use \(y_2-mx_2=b\)

Answer 24

Wait so

Answer 25

When I'm trying to find the equation for 2pm to 3pm

Answer 26

I know the slope is -400

Answer 27

y=-400x + b

what x and y values do i plug in

Answer 28

Any point on the line.

Answer 29

and I do need to create two distinct equations? or just one

Answer 30

Well, you have solve for \(m\) the normal way and just use one, I guess

Answer 31

So y=-400x + b, then plugging in a point on the line that i'm trying to find

800=-400(3)+b

Answer 32

\((x,y) = (2,1200)\)

Answer 33

Or \((x,y)=(3,800)\)

Answer 34

so b = -400

Answer 35

no no it would be b=2000

Answer 36

Yes

Answer 37

So this will allow you to solve for \(p(3)\)

Answer 38

then I do, 4, 5, add them all up, and then subtract the number of people who have gotten on the ride, correct?

Answer 39

Yes

Answer 40

We can use the fact\[
p(5) - p(0) = (p(2)-p(0)) + (p(3)-p(2)) + (p(4)-p(3)) + (p(5)-p(4))
\]

Answer 41

I don't understand, I thought I'm just using integrals for each one then adding up each integral