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heathernelly

  • 2 years ago

:)

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  1. JakeV8
    • 2 years ago
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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"?

  2. JakeV8
    • 2 years ago
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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.

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

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

  5. heathernelly
    • 2 years ago
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    yeah, that's it :)

  6. phi
    • 2 years ago
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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?

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

  8. heathernelly
    • 2 years ago
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    hmm, not really.. :///

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

  10. heathernelly
    • 2 years ago
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    okay

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

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

  13. phi
    • 2 years ago
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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"

  14. heathernelly
    • 2 years ago
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    no it doesnt :(

  15. heathernelly
    • 2 years ago
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    ahhh, this is confusing to me

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

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

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

  19. heathernelly
    • 2 years ago
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    so the pi would cancel out?:S:/

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

  21. heathernelly
    • 2 years ago
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    yeaah, thats what i thought :))

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

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

  24. phi
    • 2 years ago
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    1/980

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

  26. heathernelly
    • 2 years ago
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    k 1 sec

  27. heathernelly
    • 2 years ago
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    okays (:

  28. phi
    • 2 years ago
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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?

  29. heathernelly
    • 2 years ago
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    ohhh, yeah i did

  30. phi
    • 2 years ago
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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

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

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

  33. heathernelly
    • 2 years ago
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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?:/

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

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

  36. phi
    • 2 years ago
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    do you know how to "solve" for t?

  37. heathernelly
    • 2 years ago
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    multiply both sides by 245?:S

  38. heathernelly
    • 2 years ago
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    im not sureee :(

  39. phi
    • 2 years ago
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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?

  40. heathernelly
    • 2 years ago
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    yeaah i have

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

  42. phi
    • 2 years ago
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    I would take the square root of both sides

  43. heathernelly
    • 2 years ago
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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

  44. phi
    • 2 years ago
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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

  45. heathernelly
    • 2 years ago
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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

  46. phi
    • 2 years ago
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    Just draw a big square root over each side

  47. heathernelly
    • 2 years ago
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    |dw:1354152167387:dw|

  48. phi
    • 2 years ago
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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 ?

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

  50. phi
    • 2 years ago
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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 \[ t= \sqrt\frac{ \pi^2 L}{245} \]

  51. phi
    • 2 years ago
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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?

  52. heathernelly
    • 2 years ago
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    yes?.....

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

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

  55. phi
    • 2 years ago
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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 \[ \sqrt{\pi^2} \] ?

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

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

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

  59. heathernelly
    • 2 years ago
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    or sqaure root pie? :S

  60. heathernelly
    • 2 years ago
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    or neither? hahaa

  61. phi
    • 2 years ago
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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"

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

  63. heathernelly
    • 2 years ago
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    pi..lol

  64. phi
    • 2 years ago
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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)?

  65. heathernelly
    • 2 years ago
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    hahah!

  66. heathernelly
    • 2 years ago
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    49

  67. phi
    • 2 years ago
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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.

  68. heathernelly
    • 2 years ago
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    yeaah

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

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

  71. phi
    • 2 years ago
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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) \[ t = \frac{ \pi\sqrt{L}}{7\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}= \frac{ \pi\sqrt{5L}}{35}\]

  72. phi
    • 2 years ago
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    that is your answer

  73. heathernelly
    • 2 years ago
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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?

  74. phi
    • 2 years ago
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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)

  75. phi
    • 2 years ago
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    I am an engineer for a living..

  76. heathernelly
    • 2 years ago
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    thats awesome :D

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