Question

WILL FAN AND MEDAL!!!NEED HELP ASAP

Answer 1

Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.

Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95

Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Answer 2

why did you reopen this question? let me remind you that's against the rules.

plot the graph and see where they meet then read off the year from the graph

for the graph the width is on the y-axis and the year on the x-axis

Answer 3

@triciaal verry sorry i meant to put fan and medal

Answer 4

so did you find the approximate intersection?
ok bye

Answer 5

@Catseyeglint911 @hero @phi please help!

Answer 6

let x be the year, and y the feet
so that you can form pairs.
example, using the first beach,
(0,100)
(5,90)
(10,80)
and so on.

can you find the slope between the first two points? using change in y divided by change in x ?

Answer 7

@phi 18?

Answer 8

can you show me how, using
(0,100)
(5,90)

Answer 9

the first one is 100? and the second one is \[90\div5=18\]

Answer 10

first do change in y (y is the 2nd number in the pair.
from (0,100) you pick the y value 100
from (5,90) you pick the y value 90
now find 100 - 90

Answer 11

ohhh so 10

Answer 12

that is change in y

we now need change in x
from (0,100) you pick the x value
from (5,90) you pick the the x value
then find the difference
can you do that ?

Answer 13

yeah, its -5

Answer 14

now the slope is change in y divided by change in x
10/-5 = -2

If we plot your points, they will make a line with a slope of -2

Answer 15

ohh that makes a lot of sense!

Answer 16

Can you do the same for the second beach ?

Answer 17

I think so

Answer 18

btw, here is a plot of the first beach's line

Answer 19

umm is it 11 for y?

Answer 20

\[11\div-5=-2.2\]?

Answer 21

first, what is the first pair of numbers to use for (x,y) for the second beach
any idea ?

Answer 22

x will still be the year, and y will be from the second beach

Answer 23

(0,20),(5,45)

Answer 24

looks good

now do change in y

Answer 25

20-45=-25

Answer 26

yes, now change in x

Answer 27

-5

Answer 28

ohh so its 5

Answer 29

yes, slope is 5

It's always good to check another pair to see we get the same slope
the last two points are
(12,80)
(15,95)

can you find the slope for that pair?

Answer 30

5

Answer 31

and if we use the first and last points
(15,95)
(0, 20)
95-20 = 75
15 - 0 = 15
75/15 = 5

these all have the same slope. Here is the picture

Answer 32

So which part is that the answer to

Answer 33

the slope tells us how much the beach changes width each year.
beach one loses 2 feet every year
beach two grows 5 feet every year

Answer 34

ohh ok

Answer 35

the answer to the first part:
beach one loses 2 feet every year
beach two grows 5 feet every year

their widths can be plotted on a straight line that cross.

any idea where they cross (what year)?

Answer 36

between year 11 and 12 right?

Answer 37

yes. It's "common sense" in year 11 beach one is bigger than beach two (78 > 75)
and the next year beach one is smaller (poor beach!), so they crossed sometime between 11 and 12

Answer 38

yes poor beach is shrinking..... s thta is the answer to part 2?

Answer 39

yes

Answer 40

So what about part 3, how do i answer that?

Answer 41

I don't know what they are thinking, but I would find where the lines cross.

the first line (using point-slope form) has the equation
y - 100= -2(x- 0) or more simply
y = -2x +100

the second line has the equation
y - 20= 5(x-0) or
y = 5x+20

the cross when they have the same y value, so set the two y values equal
-2x +100 = 5x +20

solve for x (the year when they are the same size)

Answer 42

can you do that ?

Answer 43

or is it too confusing?

Answer 44

i think, so i have to find x?

Answer 45

but what year are they the same size

Answer 46

ohh thats what im solving for, derr

Answer 47

good start but (unfortunately) details matter
it's
-2x +100 = 5x +20


you started with -2x - 100 (gack! )

Answer 48

ughhh

Answer 49

\[7x=80\]

Answer 50

now divide both sides by 7

Answer 51

11.43?

Answer 52

if you round. or 11 3 / 7
that is the exact time when both beaches have the same size.
you can use either equation to find the y value (size of the beach) and you will get the size (but we don't need that.... , just the time)

Answer 53

Okay, thanks sooo much!

Answer 54

yw

Answer 55

oh, just in case they are picky,
the *year* is 1995 added to 11 for part b) 2006
and for part c ) 2006 and 3/7 (roughly 5 months)

Answer 56

oh thanksXD