math homework plz help?
it is taken from the book precalculus by
demana waits foley kennedy
chapter 4 section 4.4
page 394
exercise 72
what it sais is:
a signal buoy in chesapeake bay bobs up and down in the height h of its transmitter above sea level
modeled by h = a sin bt + 5
during a small squall its height variesfrom 1ft to 9ft and there are 3.5 sec from one 9ft height to the text. what are the values of the constants a and b,
if you dont know how to actually solve it plz give either
an idea
or if you know a site online where to find answers
thanks
thank you a lot
only a simple correction
(5+a) – (5-a) = 9 – 1 not 9+1
2a = 8 not 10
a = 4 not 5
i think that that does not affect the rest
It took me quite a while before I understood you actually wanted to write “from one 9ft to the next” (not “text”)!
Once you realize that the sin() function has a range of [-1, 1], you know that the function a*sin() will have a range of [-a,+a]. So what will the range be for h = a sin(bt) + 5?
The answer is: [5-a, 5+a]
Now it is given that the height varies from 1ft to 9ft, so with that you can find the value for a:
5-a = 1
5+a = 9
Subtract the first equation from the second and you get 2a = 10, or a = 5.
Now the value for b.
The function sin() has a cycle of 2π, meaning that sin(x) = sin(x+2π). So if after a certain time h is again the same (from 9ft to 9ft), it means the argument of the sine has become 2π greater. Lets say our stopwatch starts when the bouy hits 9ft the first time (stopwatch reads 0 s), and we stop it when it is there the second time (and it reads 3.5 s). Then we have the following equations:
b*t – b*0 = 2π, or bt = 2π
t – 0 = 3.5, so t = 3.5
So b = 2π/3.5
NB: it is not clear from the question if the argument of the sine is expressed in radians or grades. I assumed the first, but if it is the second, then you must replace 2π with 360 in the above equations.
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