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heathernelly

:)

  • one year ago
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  1. JakeV8
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    Is this actually a physics or math project or just a question asking for you to solve for the variable "t"?

    • one year ago
  2. JakeV8
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    you can use basic algebra to solve for t by isolating it, but it will be an equation using L. But that might be all you need to do... sort of depends on what the purpose of this question is.

    • one year ago
  3. heathernelly
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    just have to solve for t.. i think :/ sorry my computer is lagging!

    • one year ago
  4. JakeV8
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    \[L = \frac{ 980t^{2} }{ 4\pi^{2} }\]

    • one year ago
  5. heathernelly
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    yeah, that's it :)

    • one year ago
  6. phi
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    here is an example http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/v/solving-for-a-variable The first step is multiply both sides by 4\(\pi\). Can you do that?

    • one year ago
  7. phi
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    The first step is multiply both sides by 4\(\pi^2\). Can you do that?

    • one year ago
  8. heathernelly
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    hmm, not really.. :///

    • one year ago
  9. phi
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    write \(4 \pi^2\) times on both sides of the equation

    • one year ago
  10. heathernelly
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    okay

    • one year ago
  11. heathernelly
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    like i dont understand it because it has the pi? :/ i suck at math

    • one year ago
  12. phi
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    pi is just a number if you multiply both sides by 4 pi^2 you get \[ 4 \pi^2 L = 4 \pi^2 \cdot \frac{980 t^2}{4 \pi^2}\]

    • one year ago
  13. phi
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    now use a simple rule: if you see something divided by itself , it becomes 1. Does that ring a bell? It makes the right side "simplify"

    • one year ago
  14. heathernelly
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    no it doesnt :(

    • one year ago
  15. heathernelly
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    ahhh, this is confusing to me

    • one year ago
  16. phi
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    Here are some examples \[ 3\cdot \frac{4}{3} = \frac{3\cdot 4}{3}= \frac{\cancel{3}\cdot 4}{\cancel{3}}=4\]

    • one year ago
  17. phi
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    do you see anything in your problem that "cancels"?

    • one year ago
  18. heathernelly
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    yeah, i get that but it has the pi in the one im doing? :/

    • one year ago
  19. heathernelly
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    so the pi would cancel out?:S:/

    • one year ago
  20. phi
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    \[ 4 \pi^2 L = \cancel{4 \pi^2} \cdot \frac{980 t^2}{\cancel{4 \pi^2}} \]

    • one year ago
  21. heathernelly
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    yeaah, thats what i thought :))

    • one year ago
  22. phi
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    it is a good rule to remember. now multiply both sides by \(\frac{1}{980} \)

    • one year ago
  23. heathernelly
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    one over what? i can't read that:((

    • one year ago
  24. phi
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    1/980

    • one year ago
  25. phi
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    first write it down: \[ 4 \pi^2 L \cdot \frac{1}{980}= 980t^2 \cdot \frac{1}{980} \]

    • one year ago
  26. heathernelly
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    k 1 sec

    • one year ago
  27. heathernelly
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    okays (:

    • one year ago
  28. phi
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    the 980's cancel on the right side, right? (that is why we did this) we get \[ t^2 = \frac{4\pi^2 L}{980} \] Do you see how we did that?

    • one year ago
  29. heathernelly
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    ohhh, yeah i did

    • one year ago
  30. phi
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    the 4 pi^2 L is on the top, and when we multiply fractions, it is top times top and bottom times bottom

    • one year ago
  31. phi
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    \[ \frac{4 \pi^2 L}{1} \cdot \frac{1}{980} = \frac{4 \pi^2 L\cdot 1}{1 \cdot 980} = \frac{4 \pi^2 L}{980}\]

    • one year ago
  32. phi
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    I would simplify by dividing the top by 4, and the bottom by 4. Can you do that?

    • one year ago
  33. heathernelly
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    all of the top?:S i dont know how to simplify because the pi is there? do i use 3.14?:/

    • one year ago
  34. phi
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    leave pi alone. if you divide the top by 4 it is doing this \[ \frac{\cancel{4}\pi^2L}{\cancel{4}}\]

    • one year ago
  35. phi
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    now divide the bottom by 4: 980/4 is 245 we get \[ t^2= \frac{\pi^2 L}{245} \]

    • one year ago
  36. phi
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    do you know how to "solve" for t?

    • one year ago
  37. heathernelly
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    multiply both sides by 245?:S

    • one year ago
  38. heathernelly
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    im not sureee :(

    • one year ago
  39. phi
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    if you multiply both sides by 245 you would get a 245t^2 (making it more "complicated" ) Have you heard of a square root?

    • one year ago
  40. heathernelly
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    yeaah i have

    • one year ago
  41. phi
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    square roots are how you "undo" squares: \[ \sqrt{x^2}= x\]

    • one year ago
  42. phi
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    I would take the square root of both sides

    • one year ago
  43. heathernelly
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    can you draw it out for me so i can see what you mean? it makes more sense when you do that:D

    • one year ago
  44. phi
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    I've noticed it's easier to do work when someone else is doing it, too. try, it won't hurt

    • one year ago
  45. heathernelly
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    it really does help when someone else shows you, but ill draw it on here to see if im right :) im prob not thou ...haha

    • one year ago
  46. phi
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    Just draw a big square root over each side

    • one year ago
  47. heathernelly
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    |dw:1354152167387:dw|

    • one year ago
  48. phi
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    yes, by the t^2 is inside the root sign. and so is the 245. now use the idea that sqrt(x^2) is x so sqrt(t^2) is ?

    • one year ago
  49. heathernelly
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    245? haha.. im not sure :/ or 15? :S

    • one year ago
  50. phi
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    no, not a number. square root of x*x is x square root of t*t is t (I guess you have to memorize that) we get \[ t= \sqrt\frac{ \pi^2 L}{245} \]

    • one year ago
  51. phi
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    now, you can "simplify" (just to show off how much math you know) use the rule that sqrt(a * b) is the same as sqrt(a) * sqrt(b) so the top is sqrt(pi^2) * sqrt(L) you can simplify sqrt(pi^2) , right?

    • one year ago
  52. heathernelly
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    yes?.....

    • one year ago
  53. phi
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    use the same rule as for sqrt(x^2) (or sqrt(t^2) for that matter)

    • one year ago
  54. heathernelly
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    i dont understand when you say sqrt)x^2) really..

    • one year ago
  55. phi
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    we start with \[ t= \sqrt\frac{ \pi^2 L}{245} \] we can "break up" the square root by separating it: \[ t = \frac{ \sqrt{\pi^2}\sqrt{L}}{\sqrt{245}} \] the rule "sqrt(x^2) = x means when you see "something" to the 2nd power inside a square root , you can replace it with just "something" There is a good reason to learn this, but first what is \[ \sqrt{\pi^2} \] ?

    • one year ago
  56. phi
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    or, another way to think of it, sqrt undoes the square

    • one year ago
  57. heathernelly
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    ooh, that kinda makes more sense. what do you mean what is it?

    • one year ago
  58. heathernelly
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    so it would be pi^2?

    • one year ago
  59. heathernelly
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    or sqaure root pie? :S

    • one year ago
  60. heathernelly
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    or neither? hahaa

    • one year ago
  61. phi
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    sqrt(pi^2) is not pi^2 (that would mean sqrt is doing nothing) sqrt(pi^2) is not sqrt(pi) (that would mean pi^2 is the same as pi) sqrt(pi^2) "makes the square go away"

    • one year ago
  62. phi
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    if \[ \sqrt{x^2}= x\] and \[ \sqrt{t^2}=t\] what is \[ \sqrt{\pi^2}= ?\]

    • one year ago
  63. heathernelly
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    pi..lol

    • one year ago
  64. phi
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    yes, so now you have \[ t = \frac{ \sqrt{\pi^2}\sqrt{L}}{\sqrt{245}} \] \[ t = \frac{ \pi\sqrt{L}}{\sqrt{245}} \] finally we can rewrite sqrt(245) as sqrt(5*7*7) or \[ \sqrt{7^2}\cdot \sqrt{5} \] do I dare ask what is sqrt(7*7)?

    • one year ago
  65. heathernelly
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    hahah!

    • one year ago
  66. heathernelly
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    49

    • one year ago
  67. phi
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    7*7 = 49 but sqrt(7*7) is 7 (or sqrt(49) is 7) 7*7 is 7^2 and the square root undoes the square.

    • one year ago
  68. heathernelly
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    yeaah

    • one year ago
  69. phi
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    we now have \[ t = \frac{ \pi\sqrt{L}}{\sqrt{245}} \] \[ t = \frac{ \pi\sqrt{L}}{7\sqrt{5}}

    • one year ago
  70. phi
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    \[t = \frac{ \pi\sqrt{L}}{7\sqrt{5}} \]

    • one year ago
  71. phi
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    The last step. People (why?) do not like sqrt in the denominator, so we multiply top and bottom by sqrt(5) \[ t = \frac{ \pi\sqrt{L}}{7\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}= \frac{ \pi\sqrt{5L}}{35}\]

    • one year ago
  72. phi
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    that is your answer

    • one year ago
  73. heathernelly
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    wow, that is a loooot of work!! but thank you so much.. when i re-read over it tomorrow, i'll prob be awesome at it ;) haha....ill prob get it! :D are you a teacher?

    • one year ago
  74. phi
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    The reason you learn this is to 1. See if you *can* learn it. 2. If you can learn it, it changes how you think (in a good way)

    • one year ago
  75. phi
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    I am an engineer for a living..

    • one year ago
  76. heathernelly
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    thats awesome :D

    • one year ago
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