Page 2 of 49 FirstFirst 12345678910111227 ... LastLast
Results 21 to 40 of 976

Thread: Need help with science/math schoolwork? Post here!

  1. #21
    chris_uk_83's Avatar Physicist
    Join Date
    Feb 2007
    Location
    Lancaster, England
    Posts
    818

    Default Re: Need help with science/math schoolwork? Post here!

    Here's the link to where I found the answer. Seemingly you create the angle psi using tan(psi) = x/a and then get rid of your tan by cancelling things. I can't read that formula stuff though because I don't know the language it's written in. Feel free to have a go yourself though.

    EDIT: the link would help! http://www.physicsforums.com/archive...p/t-88325.html

    If I've helped you, rep me. I live for rep.

  2. #22
    Simetrical's Avatar Former Chief Technician
    Patrician

    Join Date
    Nov 2004
    Location
    θ = π/0.6293, φ = π/1.293, ρ = 6,360 km
    Posts
    20,154

    Default Re: Need help with science/math schoolwork? Post here!

    Quote Originally Posted by chris_uk_83 View Post
    I just looked at this thread again, and I had awful trouble reading that maths. Does anyone know of an easier way of posting mathematical equations? I'd suggest using MS Word's equation editor (which most people probably have) and attaching the word file. There must be an easier way than this though.
    Better to attach a screenshot of that. I could install a LaTeX extension at some point, but that's not high on my to-do list.
    Quote Originally Posted by ROMANUS.INVICTUS View Post
    Probably,Chris.But I am going to use Microsoft Math which I got with Encarta 2007...

    Except in this one...



    Could somebody help me in determining the time period of oscillations,if a particle with -q charge is displaced from the origin to a point,x m away from the origin in a direction perpendicular to abscissa,already under the influence of two charges,+q each separated by a distance of 2a m?The given condition is that a>>x.
    Well, by Coulomb's Law, the upward force is

    F(x) = (4π·3q0r²)·cos θ

    where

    r = sqrt(a² + x²)

    and

    θ = arctan(a/rx/a).

    But we have a >> x, so r ≈ sqrt(a²) = a, and θ = arctan(10) = 90°. Then cos θ = 01. This is clearly not what was intended by saying a >> x (edit: it isn't? Hmm, maybe it is.), so I'll discard that assumption and do it properly, messy though it may be.

    Okay, so we know the force is

    F(x) = (4π·3q0(x² + a²))·x/sqrt(x² + a²) = 12πqx0(x² + a²)3/2

    by these arguments. But that's not simple harmonic motion; we can't have an x in the denominator. So I guess make it

    F(x) = 12πqx0a3.

    Supposedly the answer is then

    T = 2π sqrt(m/k),

    where

    k = 12πq0a3,

    according to the formulas Chris posted. So

    T = 2π sqrt(m/(12πq0a3)) = 2π sqrt(mε0a³/12πq) = sqrt(πa³mε0/3q)

    which is undoubtedly wrong in some crucial way. (Edit: Although it more or less agrees in form with the solution Chris linked to, just a couple of constants different.)
    Quote Originally Posted by ROMANUS.INVICTUS View Post
    You mean something like Φ=sinˉ¹[a/(a²+x²)½] or Φ=cosˉ¹[x/(a²+x²)½],as a measure for the angle unknown?But I doubt that the real answer consists of either sin or cos.Is there a different way to move about,except assuming an angle?
    Remember that a >> x! Also important is that sin θ ≈ θ for sufficiently small θ.
    Quote Originally Posted by chris_uk_83 View Post
    I can't read that formula stuff though because I don't know the language it's written in. . . .

    EDIT: the link would help! http://www.physicsforums.com/archive...p/t-88325.html
    It's LaTeX, and you should use the non-archive link, which has pretty pictures.
    Last edited by Simetrical; April 29, 2007 at 02:09 PM.
    MediaWiki developer, TWC Chief Technician
    NetHack player (nao info)


    Risen from Prey

  3. #23
    chris_uk_83's Avatar Physicist
    Join Date
    Feb 2007
    Location
    Lancaster, England
    Posts
    818

    Default Re: Need help with science/math schoolwork? Post here!

    hehe, awesome link.

    When anyone posts formulae (superscript stuff I think) like you did in that last post they completely mess up the entire text for me. Have I got some settings wrong or are they just broken?

    If I've helped you, rep me. I live for rep.

  4. #24
    Simetrical's Avatar Former Chief Technician
    Patrician

    Join Date
    Nov 2004
    Location
    θ = π/0.6293, φ = π/1.293, ρ = 6,360 km
    Posts
    20,154

    Default Re: Need help with science/math schoolwork? Post here!

    Are you using Internet Explorer? You'll need a decent browser and at least one decent font installed to see all that properly, alas.
    MediaWiki developer, TWC Chief Technician
    NetHack player (nao info)


    Risen from Prey

  5. #25

    Default Re: Need help with science/math schoolwork? Post here!

    For values in the interval [0,pi/2], what is the minimum number of terms of the power series for f(x)=cos(x) necessary to approximate the value of cos(x) with an error whose absolute value is less than 0.0001?

    (A) 4
    (B) 5
    (C) 6
    (D) 7
    (E) 8

    Can anyone help (give explanation too)? Help will be rewarded with a rep and in the future I will help them with any physics and/or calculus (that does not involve series...man I hate those).

  6. #26
    chris_uk_83's Avatar Physicist
    Join Date
    Feb 2007
    Location
    Lancaster, England
    Posts
    818

    Default Re: Need help with science/math schoolwork? Post here!

    Are you using Internet Explorer? You'll need a decent browser and at least one decent font installed to see all that properly, alas.
    Is using IE 7 a problem? Do I need Firefox to see these properly? Or do I just need to find the right font to install. If so can you point me in the direction of a donwload link?

    @DK
    I'm useless at series I'm afraid, but try Wolfram Mathworld or Hypermath. Those were what I used to help me with maths when I got stuck. You could also try Wikipedia, which is usually very accurate with maths and physics based material and has helped me on many occasions.

    If I've helped you, rep me. I live for rep.

  7. #27
    therussian's Avatar Use your imagination
    Join Date
    Sep 2004
    Location
    Charlotte, NC USA
    Posts
    12,123

    Default Re: Need help with science/math schoolwork? Post here!

    Quote Originally Posted by DarkKnight View Post
    For values in the interval [0,pi/2], what is the minimum number of terms of the power series for f(x)=cos(x) necessary to approximate the value of cos(x) with an error whose absolute value is less than 0.0001?

    (A) 4
    (B) 5
    (C) 6
    (D) 7
    (E) 8

    Can anyone help (give explanation too)? Help will be rewarded with a rep and in the future I will help them with any physics and/or calculus (that does not involve series...man I hate those).
    Well, the answer is either A or B, because I get that the first term that gets you <.0001 error is x8/8!, which is the fifth term of the series

    Now, to get this, you have to know the power series of cos, whose general term is ((-1)nX2n)/(2n)!

    So, the power series is 1 - x2/2! + x4/4! - x6/6! + x8/8! .......and so on.

    I'm pretty sure it's B, but someone can check me on that.

    House of the Caesars | Under the Patronage of Comrade Trance Crusader. Proud Patron of Comrades Shadow_Imperator, Zenith Darksea, Final Frontier and Plutarch | Second Generation| ex-Eagle Standard Editor| Consilium de Civitate | Album Reviews

  8. #28
    Simetrical's Avatar Former Chief Technician
    Patrician

    Join Date
    Nov 2004
    Location
    θ = π/0.6293, φ = π/1.293, ρ = 6,360 km
    Posts
    20,154

    Default Re: Need help with science/math schoolwork? Post here!

    Quote Originally Posted by chris_uk_83 View Post
    Is using IE 7 a problem? Do I need Firefox to see these properly? Or do I just need to find the right font to install. If so can you point me in the direction of a donwload link?
    Ah, I see. IE was unhappy with my attempt at customization of <sup> and <sub> tags. It should show up all right now.
    Quote Originally Posted by Bulgaroctonus View Post
    Well, the answer is either A or B, because I get that the first term that gets you <.0001 error is x8/8!, which is the fifth term of the series

    Now, to get this, you have to know the power series of cos, whose general term is ((-1)nX2n)/(2n)!

    So, the power series is 1 - x2/2! + x4/4! - x6/6! + x8/8! .......and so on.

    I'm pretty sure it's B, but someone can check me on that.
    I get

    1 − (π/2)²/2! + (π/2)4/4! − (π/2)6/6! = −0.0008945...

    1 − (π/2)²/2! + (π/2)4/4! − (π/2)6/6! + (π/2)8/8! = 0.00002474...

    So it should be five terms, yes. (I don't know if there's any more theoretical way to do this. I just used a calculator, obviously, which may not be good enough for DarkKnight's teacher . . .)
    MediaWiki developer, TWC Chief Technician
    NetHack player (nao info)


    Risen from Prey

  9. #29
    therussian's Avatar Use your imagination
    Join Date
    Sep 2004
    Location
    Charlotte, NC USA
    Posts
    12,123

    Default Re: Need help with science/math schoolwork? Post here!

    Nah, I think that's the only way to do it. SHould be good enough though.

    House of the Caesars | Under the Patronage of Comrade Trance Crusader. Proud Patron of Comrades Shadow_Imperator, Zenith Darksea, Final Frontier and Plutarch | Second Generation| ex-Eagle Standard Editor| Consilium de Civitate | Album Reviews

  10. #30

    Default Re: Need help with science/math schoolwork? Post here!

    Thanks, may the rep fairy bless you. (it was a graphing calculator problem so I think you are right).

  11. #31
    chris_uk_83's Avatar Physicist
    Join Date
    Feb 2007
    Location
    Lancaster, England
    Posts
    818

    Default Re: Need help with science/math schoolwork? Post here!

    Ah, I see. IE was unhappy with my attempt at customization of <sup> and <sub> tags. It should show up all right now.
    Like a dream

    If I've helped you, rep me. I live for rep.

  12. #32

    Default Need help with high school math

    TWCers seem like an educated group, so I figure one or two of you might take the time to explain some of these to me.





  13. #33

    Default Re: Need help with high school math

    Really, come on.
    I'll settle for just the first one.





  14. #34

    Default Re: Need help with high school math

    I got half of them. I'll post the rest in a bit.

    1. I'm not entirely sure what your teacher wants but here is what I was able to do. Write out the first couple terms of the series along with the nth term. You will notice that you have "n" number of "1"s. This is due to the 1 that gets added for every term. You can pull that 1 out of the sigma as an n. So it becomes n + sigma(2i/n). Then the n is a constant so you can pull it out of the sigma now. The simplfied form is: n + (1/n)sigma(2i).

    2. arcsin(-1/2)= -pi/6
    2*-pi/6= -pi/3
    cos(-pi/3)= 1/2

    3. Draw a right triangle designate one leg with a legnth of 1 and the other with a legnth of x. Find the angle whose tan=x (the one next to the 1). Then find the angle whose tan=1/x (the one next to the x). So you are adding up the two non 90 degree angles, which of course will add up to 90 degrees because there are 180 degrees in a triangle. But normally these kinds of problems want radians, so the radian equivalent of 90 degrees is pi/2.

    4. Convert the equation to exponentional form.
    10^2 = x^2 - 3x
    Now solve for x
    x^2 - 3x - 100 = 0
    Quadratic equation
    (9 +/- sqrt(9+400))/2
    (9 +/- sqrt(409))/2
    I don't have my calculator handy to give a decimal approximation.

    5. I had a bit of trouble reading this one. It looks like 4^(3-4x)>=1
    If that is the correct equation it is solved like so.
    Take the log of each side.
    log(4^(3-4x))>=log(1)
    Pull the exponent out in front of the log and evaluate the log(1)=0
    (3-4x)log(4)>=0
    (3-4x)>=0
    4x<=3
    x<=3/4

  15. #35
    mrmouth's Avatar flaxen haired argonaut
    Join Date
    Apr 2007
    Location
    Chicago
    Posts
    10,741

    Default Re: Need help with high school math

    yeah, what dark knight said.

  16. #36
    sephodwyrm's Avatar Praefectus
    Join Date
    Jun 2005
    Location
    Taiwan
    Posts
    6,757

    Default Re: Need help with high school math

    Ahhh...maths...
    Chinese nerd to the rescue.
    Wait, I actually nearly failed Linear Algebra. I will print these questions out and scan them to help you.

    Btw, tell them that a mighty Chinese did it.
    Older guy on TWC.
    Done with National Service. NOT patriotic. MORE realist. Just gimme cash.
    Dishing out cheap shots since 2006.

  17. #37

    Default Re: Need help with high school math

    Bear in mind I'm not allowed any sort of graphical proof (like you suggested for number 3).





  18. #38

    Default Re: Need help with high school math

    1.
    2n-1/n-1...I used integration for this one, forgot how to do it the "normal" way.

    2.
    arcsin(-1/2) is (7*pi)/6 (you should know that by memory). Simply plug that in and you get cos((7*pi)/3), which is 1/2.

    3.
    tan(angle) is the sin(angle)/cos(angle). In the first case, it is x. In the second it is the multiplicative inverse of that. We know the tangent is positive because they tell you x>0. This means sin/cos must be positive and therefore it must be in the first or third quadrant (where +/+ or -/- is +).

    Since we know that sin(angle1)=cos(angle2) and vice versa, and sin^2+cos^2=1, we can conclude that it goes from cos=1 to sin=1. And therefore the sum of the two angles must be pi/2.

    4.
    For log functions, just remember that it's pretty much the opposite of power functions. In this one, the log base isn't displayed which means it is 10. It's telling you that 10^2=x^2-3x or 100=x^2-3x. Set it equal to zero and use the quadratic formula.

    For the rest of the log functions just use the properties. i.e. for 6 use log base 3 of te top minus the log base 3 of the bottom, and set that >0.

    I forgot most of the statistical stuff on the bottom, but it isn't hard. The book will give you a simple formula to follow.
    Last edited by PooFoo; May 17, 2007 at 09:27 PM.

  19. #39

    Default Re: Need help with high school math

    6. Convert to exponential form
    3^0 = (3x-2)/(x-2)
    1 = (3x-2)/(x-2)
    x-2 = 3x-2
    x = 3x
    2x = 0
    x = 0

    7. Take the log of each side
    log(3^x) = log(2^(3x+1))
    Pull the exponents out
    xlog3 = (3x+1)log2
    xlog3 = 3xlog2+log2
    xlog3-3xlog2 = log2
    x(log3-3log2) = log2
    x = log2/(log3-3log2)

    8. Convert to exponential
    2^-1 = log(6x)
    1/2 = log(6x)
    Convert to exponential again
    10^(1/2) = 6x
    x = sqrt(10)/6

    Hmm... I must teach myself standard deviation before continuing.

  20. #40

    Default Re: Need help with high school math

    No need to do number 10.
    As far as standard deviation goes, it is directly related to the concept of sigma (the greek letter in the first problem which forms the basis for a part of math I'm having significant trouble with).
    In fact, I'm fairly sure I got the standard deviation part correct and see no need for you to exert yourself.
    Number 1 still poses a problem to be.
    I believe I even have the answer (copied): (1+n)/2 * n





Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •