Question

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t).

Answer 1

@dtan5457

Answer 2

can any one please help me solve this step by step?

Answer 3

cant you create a chart to find d=rt?

Answer 4

what ? im sorry i dont understand :/

Answer 5

umm hold on. let me make sure Im giving you the right information

Answer 6

ok

Answer 7

Ive not worked with cos functions. im sorry Im not going to be any help here.

Answer 8

@amistre64 might be able to help

Answer 9

ok alright thanks

Answer 10

@jim_thompson5910

Answer 11

@SithsAndGiggles

Answer 12

@dtan5457

Answer 13

can one of you guys walk me through this?

Answer 14

oh ive tried helping before :)

we need to determine amplitude, and period to start things off with

Answer 15

how do we define amplitude?

Answer 16

amplitude is the highest point on the y axis which is the distance right? it has to be a positive number?

Answer 17

amplitude is half the distance between the lowest and highest values for the Y axis.

(high - low)/2 = amplitude

from the stated problem what is the amplitude?

Answer 18

these are the parts we want to determine.

midline period
vv vv
y = M + A cos( P t)
^^
amp

Answer 19

midline is the average of low and high

M = (low+high)/2



amplitude is half the height, and M is in the center, so adding M+A gives us the high point

A = high - M



period is a measure of how long it takes to repeat itself, since cos(u) has a normal period of 2pi, and we know that it takes 12 hours to go to low tide, and itll presumably take another 12 hours to get back to high tide (general assumptions); then we t=24 ..

u = Pt; when t=24, u=2pi

P(24) = 2pi must be satisfied.

Answer 20

i know that the amplitude is 5

Answer 21

@amistre64

Answer 22

good, and the midline?

Answer 23

A = high - M

we know A and high, find M

or another way, average high and low

Answer 24

what is the midline again?

Answer 25

im not going to make a long drawn out posting of repeating myself over and over when what ive already typed is sufficient. scroll up and read. if its unclear, then ask questions about what ive already stated.

Answer 26

ohhhh is it 7 ?

Answer 27

@amistre64

Answer 28

now your going to make me ... 12 + 2 14 ... yeah 7s fine :)

Answer 29

so far we have:

y = 7 + 5cos(u) just have to determine u = Pt for the period ...

Answer 30

so, 24=2pi do i simplify this? or factorize it ?

Answer 31

24 P = 2pi, its a basic algebraic process to find P ...

Answer 32

do i divide by 24 at both sides to isolate the variable?

Answer 33

correct

Answer 34

so P= 2pi/24

Answer 35

or simply P = pi/12

now put the equation together

y = M + A cos(Pt)

Answer 36

do i simplify this?

Answer 37

but pi over twelve isnt any of my options

Answer 38

@amistre64 isnt there a way ti simplify it more?

Answer 39

it*

Answer 40

i dont know what your options are

Answer 41

here they are

Answer 42

t it be c?

Answer 43

it takes 12 hours to go from high to low, so it would take 24 hours to go from high to high; P 24 = 2pi when P = pi/12

Answer 44

Assuming the next high tide is exactly 12 hours later

i misread the info .....

pi/6 is fine

Answer 45

C is the most likely option since it fits the Midline and Amp as determined .... and pi/6 is good is correct when we do the actual problem instead of making things up lol

Answer 46

XD thanks a lot for your help :-)

Answer 47

your welcome :)