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OfflinephEight
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urgent math problem i need help getting solved
    #3999264 - 04/01/05 10:46 AM (12 years, 8 months ago)

Hello all, this problem has been cauing me to pull my bloody hairs out..

Naturalists find that the poplulations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when time t = 0. A minimum number, 200 foxes, occured when t = 2.9 years. The next maximum, 800 foxes, occured at t = 5.1 years.

a.) Sketch a graph of this sinuoid.
b.) Write an equation expressing the number of foxes as a function of time,
t.
c.) Predict the population when t = 7
d.) Foxes are declared to be an endangered species when their population drops below 300. Between what two non-negative values of t were foxes first endangered?

I do not know how this graph should look like... as in whether it should be sine or cosine, and how I would properly show the minimums and maximums. Any help with any aspect of this problem would be greatly appreciated, thanks.


--------------------
"Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood." -Ralph Waldo Emerson


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999277 - 04/01/05 10:50 AM (12 years, 8 months ago)

Damn! I just had a quiz on this yesterday...give me few minutes


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OfflinephEight
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Re: urgent math problem i need help getting solved [Re: Boom]
    #3999288 - 04/01/05 10:52 AM (12 years, 8 months ago)

thanks man


--------------------
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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999293 - 04/01/05 10:54 AM (12 years, 8 months ago)

>>as in whether it should be sine or cosine.

They are the same.... translate the sine along the x axis and it will be a cosine.

sin(x)=cos(x+0.5pi)


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Re: urgent math problem i need help getting solved [Re: Annom]
    #3999328 - 04/01/05 11:05 AM (12 years, 8 months ago)

Damn I had trig last semester, can't remember shit... :frown:

As Annom said, you can write two equations, one with sin or cosine, and they;ll both be 100% right, just that the sin starts at the origin, and the cosine starts at the maximum, and falls.

Sin=cosine, just cosine is shifted half a period to the left

I forget how to make formuals, but you have everything you need...

The graph is shifted up so that the max is 800 and the min is 200, so I think in the equation the max would be 300??

I'm sorrrry :shrug:


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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999343 - 04/01/05 11:09 AM (12 years, 8 months ago)

number of foxes(t) = 300*cos[pi/2.2(t-5.1)]+500


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OfflinephEight
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Re: urgent math problem i need help getting solved [Re: Boom]
    #3999347 - 04/01/05 11:10 AM (12 years, 8 months ago)

It's alright, thanks for tryin though.

How do you figure the equation to be 300? I haven't done this shit in a few months and all of a sudden we have a few problems to do as "project" thing, and this was one of them... due in 1 hour =X

For the graph, would the 200 as the minimum go below the line? I mean, doesn't the horizontal line represent 0? So it wouldn't make much sense for it to be below it. Now my question is, if it's not below it, then how am I properly supposed to draw the sin/cosine curve? I'm havin a damn hard time with this problem.

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--------------------
"Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood." -Ralph Waldo Emerson


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999351 - 04/01/05 11:11 AM (12 years, 8 months ago)

I got 200 for t=7, might be wrong tho

Dammit today is my day off from brain activity


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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999378 - 04/01/05 11:17 AM (12 years, 8 months ago)

number of foxes(t) = 300*cos[pi/2.2(t-5.1)]+500

It's hard for me to explain it in English.

The amplitude is increased by a factor 300; that's why every outcome of a normal cos has to be multiplied by 300.

The max for cos(x) is at x=0 and now it should be at 5.1; this is a translation along to x axis to the right, thus t-5.1 .

The period is 2*(5.1-2.9) = 4.4 and the normal period of cos(x) is 2pi. The period is thus increased with a factor 2pi/4.4.

And the middle point of the cos is translated along the y axis and should now be 500; thus the outcome +500.


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OfflinephEight
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999384 - 04/01/05 11:18 AM (12 years, 8 months ago)

thanks for the equation annom

booooom, do you mind explaining how you got 200 for t = 7?


--------------------
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Offlinecybrbeast
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Re: urgent math problem i need help getting solved [Re: Annom]
    #3999386 - 04/01/05 11:19 AM (12 years, 8 months ago)

I arrived at the same conclusion only I have
foxes(t) = 300*cos[pi/2.2(t-0.7)]+500


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999391 - 04/01/05 11:20 AM (12 years, 8 months ago)

The population for t=7 is ~227


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999394 - 04/01/05 11:20 AM (12 years, 8 months ago)

I wrote some shitty little graph

800 as the max, 200 as the min, where the x axis intercepts the y I called this 500.

Then I put 5.1 as the end of the period (where the max is hit) then i blah blah blah


Do what Annom said :grin:


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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: cybrbeast]
    #3999403 - 04/01/05 11:23 AM (12 years, 8 months ago)

Quote:

cybrbeast said:
I arrived at the same conclusion only I have
foxes(t) = 300*cos[pi/2.2(t-0.7)]+500




That's just one peroid(4.4) less to the right; it's the same....


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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: cybrbeast]
    #3999406 - 04/01/05 11:24 AM (12 years, 8 months ago)

Quote:

cybrbeast said:
The population for t=7 is ~227


  :thumbup:

Would you like to smoke my new Hookah with me tonight?  :cool:


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OfflinephEight
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999410 - 04/01/05 11:25 AM (12 years, 8 months ago)

lol werd

cyberbeast, can you please tell me how you got t-0.7? your equation is identical to that of annoms except for that...

also, can you please explain to me how you got ~227 for t = 7?

tahnks again guys for helpin me out!


--------------------
"Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood." -Ralph Waldo Emerson


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Re: urgent math problem i need help getting solved [Re: Annom]
    #3999411 - 04/01/05 11:25 AM (12 years, 8 months ago)

Most definately  :grin:


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999420 - 04/01/05 11:27 AM (12 years, 8 months ago)

Annom already gave the answer
Maybe this site will help you
http://math.la.asu.edu/~walker/mat170/homework/sine_curves.htm

t=7
foxes(t) = 300*cos[pi/2.2(7-0.7)]+500 = 227.1104 etc


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OfflineAnnomM
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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999433 - 04/01/05 11:30 AM (12 years, 8 months ago)

Quote:

phEight said:
lol werd

cyberbeast, can you please tell me how you got t-0.7? your equation is identical to that of annoms except for that...

also, can you please explain to me how you got ~227 for t = 7?

tahnks again guys for helpin me out!




A cosine is 'duplicated' every one period. The equation gives the same outcome at x+one period. The period of foxes(t) is 4.4. So 300*cos[pi/2.2(t-0.7)]+500 and 300*cos[pi/2.2(t-5.1)]+500 and 300*cos[pi/2.2(t-9.5)]+500 are all the same.

foxes(7)=300*cos[pi/2.2(7-0.7)]+500 = 227.11


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Re: urgent math problem i need help getting solved [Re: phEight]
    #3999439 - 04/01/05 11:31 AM (12 years, 8 months ago)

Between t=2.311 and t=3.489 the foxes were first endangered.


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