Question

Help please.

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.?

Answer 1

@jim_thompson5910 @Hero @.Sam. @robtobey @hba @campbell_st

Answer 2

well the difference in the tide is 40 half of that value gives the amplitude a = 20


so you have

\[f(x) = 20\cos(bx) + c\]

the value of c is 32... since the centre of the has been moved up 32 units so that the minimum amplitude is 12 = ( 32 - 20) and the maximum is 52 = (32 + 20)

so now you get

\[f(x) = 20\cos(bx) + 32\]

so if the curve takes 6 1/4 hours from low to high tides then it will take 12 1/2 hours to complete a full cycle.

so now you need to adjust the period... converting 12 1/2 hours to an angle measure.

Answer 3

375 degrees? I'm assuming I like envision a clock to convert that to an angle measure but I could be completely wrong

Answer 4

oops should be 12/12.5 for the value of b

Answer 5

The period will be 12.5 So

\[f(x) = -20 \cos [\frac{ 2\pi }{ 12.5 }(x-9.25)] + 32\]

Answer 6

I'm confused, is that my final answer? ^

Answer 7

the cosine curve starts at the low tide so -20 ; period is 12.5 so 2pi /12.5 and the curve is shifted 9.25 to the right so (x-9.25) and it is shifted 32 up so +32. Am I right @campbell_st

Answer 8

I am 99 % sure that is right

Answer 9

@campbell_st I'm confused, what do I plug in for the value of b? .96? (12/12.5)

Answer 10

consider the clock has 24 segments for 24 hours. So one whole day is 2pi one full rotation. you divide that into period of 12.5 hrs. so 2pi / 12.5

Answer 11

How come he has 20cos up above and you have -20cos?

Answer 12

and x is not just x because the graph is transformed to the right meaning shifted to the right by 9.25 ( starting of the low tide)

Answer 13

-20 meaning it starts with the low tide. The middle is 32 , the low point is at 12 which is 20 down so -20 then it goes up.

Answer 14

Ok, thanks :)... one more thing, my problem asks me to show work, do you know what kind of work I can show for this problem?

Answer 15

you can draw the graph

Answer 16

I can't draw anything in my applet

Answer 17

you can use explanation given my @campbell_st with the minor corrections I gave and show your work that way

Answer 18

for the most part of it he is right. how he got the 20, the 32 etc. You add the -ve sign and the explanation I gave you for finding the b and also the transformation of x to x-9.25 etc. and write you answer

Answer 19

thanks

Answer 20

@rajee_sam I really think that it is positive 20 cos not -20.... the amplitude can't be negative

Answer 21

amplitude is not negative the direction is negative

Answer 22

y=ACos(Bx-C)

A=amplitude
B=coefficient of x
Period=2pi/B
Phase shift=C/B

Answer 23

I don't see how the direction matters in the equation, it's just plug in for a, or the amplitude, which is 20

Answer 24

in a day the first one that starts the cos curve is the low tide which is -20 from the mean