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    Our Solar System name?

    Ok, so I've been passionately researching my latest novel idea as it takes place in an extremely far fetched future with long range interstellar travel and all that and the brink of controlled time modulation etc... While doing this, I've been able to name every site, system, planet of...
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    Rawr! Stuck on ODE (linear 1st order!)

    Thank you so much guys, I was banging my head on my desk with that. The solution y = \frac{(x+8)^{9}}{13} + (8^{5} - \frac{8^{13}}{13})(x+8)^{-4} checked out.
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    Rawr! Stuck on ODE (linear 1st order!)

    No luck. Oh well, thanks for your time I guess.
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    Rawr! Stuck on ODE (linear 1st order!)

    Ok lemme look at that, thanks.
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    Rawr! Stuck on ODE (linear 1st order!)

    I didn't think it'd matter... I get the same thing. y = \frac{(x+8)^{9}}{13} + C_{1} | where C_{1} is just another arbitrary constant that will satisfy the equation given the initial conditions. I get the same constant regardless... 8 = \frac{8^{9}}{13} + C_{1} C_{1} = 8 -...
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    Rawr! Stuck on ODE (linear 1st order!)

    Homework Statement Solve the initial value problem: y'+\frac{4y}{x+8}=(x+8)^{8} , y(0)=8. The differential equation is linear. Homework Equations N/A The Attempt at a Solution I can see that the equation is in the form y' +P(x)*y = Q(x) so I'm like "easy, lemme get an...
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    What should I do to get into MIT, CalTech, etc?

    Two-Fish I thoroughly enjoyed your edgy, quasi-Yoda-like contributions to what may have been just some ordinary necro thread!
  8. O

    2log(x-1) + logx = logx + log4

    There you go! I'd have kept log(4) on the right side and then just solve for x.
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    2log(x-1) + logx = logx + log4

    Well the first step is just an algebra step, you have log (x) on both sides of the = sign, so the equation can be reduced. When that happens you are left with a log (of something) = log (of something else) when this happens you can sort of drop the log and just solve for x.
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    2log(x-1) + logx = logx + log4

    Hey there, ok it looks like you have some exact same term on both sides to begin with, so those can just cancel out right? This leaves you with a log of something = a log of something else, that should simplify it down nice for ya.
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    Improper Integral (Calc II)

    Ugh... Sorry to waste your time. The limit is pi/2, all I had to do was take the limit and I was already done lol. For some reason I thought there would be no limit for the arctan and that was bothering me.
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    Improper Integral (Calc II)

    Been doing some calculus review to knock the rust off for this coming fall semester and I got stuck... Homework Statement From Stewart's book (Early Transcendentals: 6E): (7.8 pg517 #69) Determine how large the number "a" has to be so that: \int\stackrel{\infty}{a}\frac{1}{x^{2}+1}dx <.001...
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    Vector Question(addition?)

    Although, my answer is wrong Hmm, I just gave this a shot myself and got the same magnitude for the r vector, it looks correct to me...! What did you get for the angle?
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    Two algebra (1?) problems

    Hey Cyril, I think Mark pretty much covered everything but I wanted to chime in about coefficients as it sounds like you're just getting your pinky toe wet with Algebra. The 0.06x from your first problem has two parts and you were correct in that they are multiplied together (the number and...
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    Frustrated about a minus in the result (D = RT question)

    I may have approached this differently... DA + DB = 25 Where D is just the distance traveled per person and equal to rate*time. I got a positive solution using this method - something for you to take a look at if you'd like.
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    Simplify a fraction

    Here's a little something to look at: 4b2 can be written as: (2b)2 ... I think this has reverse foil written all over it. :wink:
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    Reviewing AP Calculus 1999 exam instantaneous rate problem

    I feel your frustration bro (been there). What happens when the function goes negative? (As far as integration is concerned)
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    Parametric Equations

    Hm, I'm a student myself but that looks correct to me... I would've done the same thing!
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    Building an artificial lake

    Thanks Stephen, I had briefly thought about the rising water level affecting the footprint underneath and thus affect integration. We're using MS Excel for most of the grunt work, I'm now thinking I may have to come up with a decent over/under estimation using different shapes (like a...
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    Building an artificial lake

    "Building an artificial lake" Howdy PF :smile: this is actually a Calc III project I'm working on with two others. We are in the beginning stage and are having a little trouble on how to exactly go about doing this problem... Homework Statement "A small man made lake is being proposed on...
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    Calculators TI-89 Calculator Help

    Ok, off the bat I'd recommend setting the "angle" to "Radian" for polar mode. Got the same settings on mine pretty much otherwise.
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    Can you prove the area of a circle by calculus?

    Here goes my cherry post: Being a 2nd/3rd year community college science student (transferring this fall with every intention to major in pure Math) I wanted to ask when you say "to prove" something, do you mean an actual formal proof composition? Or is just some symbolic demonstration (ie...
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