## heathernelly 3 years ago :)

1. JakeV8

Is this actually a physics or math project or just a question asking for you to solve for the variable "t"?

2. JakeV8

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

just have to solve for t.. i think :/ sorry my computer is lagging!

4. JakeV8

$L = \frac{ 980t^{2} }{ 4\pi^{2} }$

5. heathernelly

yeah, that's it :)

6. phi

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

The first step is multiply both sides by 4$$\pi^2$$. Can you do that?

8. heathernelly

hmm, not really.. :///

9. phi

write $$4 \pi^2$$ times on both sides of the equation

10. heathernelly

okay

11. heathernelly

like i dont understand it because it has the pi? :/ i suck at math

12. phi

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

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

no it doesnt :(

15. heathernelly

ahhh, this is confusing to me

16. phi

Here are some examples $3\cdot \frac{4}{3} = \frac{3\cdot 4}{3}= \frac{\cancel{3}\cdot 4}{\cancel{3}}=4$

17. phi

do you see anything in your problem that "cancels"?

18. heathernelly

yeah, i get that but it has the pi in the one im doing? :/

19. heathernelly

so the pi would cancel out?:S:/

20. phi

$4 \pi^2 L = \cancel{4 \pi^2} \cdot \frac{980 t^2}{\cancel{4 \pi^2}}$

21. heathernelly

yeaah, thats what i thought :))

22. phi

it is a good rule to remember. now multiply both sides by $$\frac{1}{980}$$

23. heathernelly

one over what? i can't read that:((

24. phi

1/980

25. phi

first write it down: $4 \pi^2 L \cdot \frac{1}{980}= 980t^2 \cdot \frac{1}{980}$

26. heathernelly

k 1 sec

27. heathernelly

okays (:

28. phi

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

ohhh, yeah i did

30. phi

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

$\frac{4 \pi^2 L}{1} \cdot \frac{1}{980} = \frac{4 \pi^2 L\cdot 1}{1 \cdot 980} = \frac{4 \pi^2 L}{980}$

32. phi

I would simplify by dividing the top by 4, and the bottom by 4. Can you do that?

33. heathernelly

all of the top?:S i dont know how to simplify because the pi is there? do i use 3.14?:/

34. phi

leave pi alone. if you divide the top by 4 it is doing this $\frac{\cancel{4}\pi^2L}{\cancel{4}}$

35. phi

now divide the bottom by 4: 980/4 is 245 we get $t^2= \frac{\pi^2 L}{245}$

36. phi

do you know how to "solve" for t?

37. heathernelly

multiply both sides by 245?:S

38. heathernelly

im not sureee :(

39. phi

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

yeaah i have

41. phi

square roots are how you "undo" squares: $\sqrt{x^2}= x$

42. phi

I would take the square root of both sides

43. heathernelly

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

I've noticed it's easier to do work when someone else is doing it, too. try, it won't hurt

45. heathernelly

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

Just draw a big square root over each side

47. heathernelly

|dw:1354152167387:dw|

48. phi

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

245? haha.. im not sure :/ or 15? :S

50. phi

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

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

yes?.....

53. phi

use the same rule as for sqrt(x^2) (or sqrt(t^2) for that matter)

54. heathernelly

i dont understand when you say sqrt)x^2) really..

55. phi

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

or, another way to think of it, sqrt undoes the square

57. heathernelly

ooh, that kinda makes more sense. what do you mean what is it?

58. heathernelly

so it would be pi^2?

59. heathernelly

or sqaure root pie? :S

60. heathernelly

or neither? hahaa

61. phi

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

if $\sqrt{x^2}= x$ and $\sqrt{t^2}=t$ what is $\sqrt{\pi^2}= ?$

63. heathernelly

pi..lol

64. phi

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

hahah!

66. heathernelly

49

67. phi

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

yeaah

69. phi

we now have $t = \frac{ \pi\sqrt{L}}{\sqrt{245}}$ $t = \frac{ \pi\sqrt{L}}{7\sqrt{5}} 70. phi \[t = \frac{ \pi\sqrt{L}}{7\sqrt{5}}$

71. phi

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

73. heathernelly

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

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

I am an engineer for a living..

76. heathernelly

thats awesome :D