Stuck on a problem- mainly due to the algebra Watch

Illidan2
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#1
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https://imgur.com/a/5gAtYbx

Part b.

It came naturally to me that I should use the quotient rule here. I proceeded to so do, and got to  \frac{1575e^{-0.25t}}{(3+7e^{-0.25t})^2} . I got stuck here, but apparently it is possible to manipulate the algebra I have here in such a way that I arrive at the printed answer. How would one go about doing this?

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mqb2766
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There is obviously a factor of N you can pull out, what remains?
Its a couple of lines of fiddling and perhaps working back from the answer isn't a bad stragegy in this case.
(Original post by Illidan2)
https://imgur.com/a/5gAtYbx

Part b.

It came naturally to me that I should use the quotient rule here. I proceeded to so do, and got to  \frac{1575e^{-0.25t}}{(3+7e^{-0.25t})^2} . I got stuck here, but apparently it is possible to manipulate the algebra I have here in such a way that I arrive at the printed answer. How would one go about doing this?

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Illidan2
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How can I pull a factor of N out of this, given the value of N?
(Original post by mqb2766)
There is obviously a factor of N you can pull out, what remains?
Its a couple of lines of fiddling and perhaps working back from the answer isn't a bad stragegy in this case.
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mqb2766
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The denominator of dN/dt is the denominator of N squared and the numerator of N is a constant. So just write
dN/dt = N*?
Then a bit of fiddling with the "?" to get it in the form (300-N)/1200
(Original post by Illidan2)
How can I pull a factor of N out of this, given the value of N?
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Illidan2
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(Original post by Illidan2)
How can I pull a factor of N out of this, given the value of N?
Okay, I have a factor of N. My bad.
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mqb2766
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Are you ok with the remainder?
(Original post by Illidan2)
Okay, I have a factor of N. My bad.
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Illidan2
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To be honest i'm still struggling. I didn't want to trouble you further so I didn't say anything. Yeah, not sure where to go after I have taken out that first factor of N.
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Last edited by Illidan2; 4 weeks ago
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mqb2766
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When you've taken out the factor of N you're left with something like
az / (bz + c)
where z is the exponential and b & c match the denominator of N. Working back from the answer, you know you want it as a partial fraction
d + e/(bz + c)
where this can be made to match e with the numerator of N (pull out a constant).

So simply divide az by (bz+c) to express in partial fractions. You'd get
a/b + r/(bz+c)
where e=r is the (constant) remainder after (polynomial) division, i.e.
-ca/b
That's pretty much it.
Last edited by mqb2766; 4 weeks ago
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