anonymous
  • anonymous
The amount of money in an investment account (in millions) is given by P(t)=-cos(4t)+39-2t where t is in months. If the amount of money ever exceeds $38 million the manager of the account receives a bonus. During the first 3 months the account is open, does the manager ever receive a bonus?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
substitute t = 1, t=2 and t =3 in the equation and see if its value exceeds 38
anonymous
  • anonymous
I understand that I'm finding this on the closed interval [1,3]. I'm having problems with finding the angle other than 4t=.5236 + 2pi(n)
anonymous
  • anonymous
Is it 4t=2.6179 + 2pi(n)?

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anonymous
  • anonymous
just because you are finding the cosine of something doesn't mean that that something is an angle. it can be time (in this case) or frequency or anything else. don't worry about converting it to an angle.
anonymous
  • anonymous
Okay I don't know quite how to explain it, but I know I have to find the other equation for the other quadrant.
anonymous
  • anonymous
why? your system is defined by the equation you are given. what is all this talk about quadrants?
anonymous
  • anonymous
Sorry dude. I don't know enough about what I'm talking about to explain. I could show you all the work I've done but I still don't know if I could convey to you what I'm talkin bout.
anonymous
  • anonymous
I'm using examples from my professor's notes to work this problem - I just know that at this point he always finds which quadrants the argument exists in and then evaluates.
anonymous
  • anonymous
Check your notes and see if in all those cases the cosine happened to be in the denominator or numerator of a fraction.
anonymous
  • anonymous
No sir
anonymous
  • anonymous
cosine of both positive and negative numbers always exists.
anonymous
  • anonymous
Right so in which quadrants is inverse sin positive?
anonymous
  • anonymous
2nd quadrant i believe
anonymous
  • anonymous
or rather, in the 1st and 4th quadrants
anonymous
  • anonymous
p(1) = -cos(4)+39-2 = 37.653 p(2) = -cos(8)+39-4 = 35.145 p(3) = -cos(12)+39-6 = 32.156. Since the principal amount does not exceed 38, the manager does not get a bonus. is that clear?
anonymous
  • anonymous
I have calculated the cosines in radians, I am not sure if you have to convert them to degrees.
anonymous
  • anonymous
That is what I got, also. Yes - I calculate only in radians. Thank you for your time/help!
anonymous
  • anonymous
There are other values besides t = 1, 2, 3... there are also values between them. As it turns out: t = .27728605 produces 38.00000001
anonymous
  • anonymous
you are welcome. It shouldn't make a difference if you are calculating in radians or degrees since cosines cannot exceed 1 on either side.
anonymous
  • anonymous
ah yes, branlegr is right! The problem stated if the manager EVER receives a bonus. you should heed branlegr's advice.
anonymous
  • anonymous
But how do you know to solve for t=.2773?
anonymous
  • anonymous
the problem is ambiguous. Does the statement t is in months mean that t can only take integer values?
anonymous
  • anonymous
Holy crap I'm so confused. Obviously not, because I solved for P(1.7010), P(2.2253)...etc

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