## anonymous 4 years ago ab=c Solve for a Do i need to divide both sides by b?

1. anonymous

yes

2. anonymous

And that is all?

3. anonymous

yes, so when you do that what will you get?

4. anonymous

a=a?

5. anonymous

$\frac{ab}{b}=\frac{c}{b}$ $a=\frac{c}{b}$

6. anonymous

Oh! now i get it, can you set up another example so i can try?

7. anonymous

Sure ax+y=c, solve for x

8. anonymous

Ok, divide ax with a, then divide c with a getting ax/a+y=c/a. You then simplify that getting x+y=c/a. Then you take both sides minus y getting x=c/a-y

9. anonymous

Is this correct?

10. anonymous

Really close but we need to either get rid of the y first before divide or also divide the y by a

11. anonymous

YES! Thanks for teaching me :)

12. anonymous

aw :(

13. anonymous

No, first start by subtracting y from both sides

14. anonymous

Alright, so ax+y=c ax=c-y x/a=c/a-y x=c/a-y

15. anonymous

remeber that when you divide the a you need to do it to all the terms

16. anonymous

Where did you get z?

17. anonymous

Oh right.. so x=c-y/a

18. anonymous

$x=\frac{c-y}{a}$

19. anonymous

zbay is correct

20. anonymous

Inopeki got the answer i just put it in the equation maker for ease of the viewers

21. anonymous

Yay! :D

22. anonymous

inopeki you need to write x=(c-y)/a just to make it clearer. i see it now good work

23. anonymous

Thanks for the help :) Is there any way you can make it a little harder to give me a challenge?

24. anonymous

yea i will come up with one for you

25. anonymous

Thanks.

26. anonymous

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$ Solve for T_2

27. anonymous

umm.. ill try

28. anonymous

Nobody mentioned division by zero ?!!

29. anonymous

Good observation @ Foolformath

30. anonymous

Well to begin with i need to multiply both sides with P2V2, getting P1V1/T1*P2V2, right?$P _{1}V _{1}divT _{1}+P _{2}V _{2}=T2$

31. anonymous

I'll lay it out by steps for you

32. anonymous

NOO. wait. Its

33. anonymous

Cross multiplication

34. anonymous

P1V1/T1*P2V2=T2

35. anonymous

lcd = T_1T_2 $T_2P_1V_1=V_2P_2T_1$ $T_2=\frac{V_2P_2T_1}{P_1V_1}$

36. anonymous

Oh right, i see it now. You wanted me to put the things i was multiplying by(V2P2) in by the other things that were multiplied. That would mean my answer is right, but yours is simplified.

37. anonymous

No?

38. anonymous

No because you need to multiply both sides by the lcd of $T_1T_2$ first then we cancel one of the varibles out because they are the same on top and bottom. then we can break T_2 apart from the rest of the left side by division, your answer would look close but in the end it would be wrong

39. anonymous

What is an lcd? What makes T1 jump up?

40. anonymous

lcd= lowest common denominator

41. anonymous

What is that?

42. anonymous

Is a denominator the 1 in T1?

43. anonymous

The denominator is what is on the bottom of the fraction, so when we do the left side we get $\frac{T_1T_2P_11V_1}{T_1}$ and because we have the same thing on the top and bottom we can cancel out the denominator leving us with $T_2P_1V_1$ and we do the same operation on the right side

44. anonymous

Why do we get T1 on both sides of the line?

45. anonymous

because you are multiplying by t1t2 but on each side one of them will cancell

46. anonymous

Ah

47. anonymous

Good job that was a hard one

48. anonymous

Thanks, when am i going to get to learn this in school?

49. anonymous

50. anonymous

8th

51. anonymous

Not sure when you will cover that but it's a chemistry equation compariing similar gasses to determine preasure, temp, or volume. You might touch it in highschool sometime.

52. anonymous

Oh, cool. What should i do now?

53. anonymous

PV=nrt solve for n

54. anonymous

And then try this $V=\frac{4}{3}\pi r^3$ Solve for r

55. anonymous

Divide both sides by rt, getting PV/rt=n, am i right? By the way, why is PV upper case?

56. anonymous

Zed, isnt that for volúmes of spheres or something? exept r should be ^3

57. anonymous

good question and i don't have an answer for you but in that equation they are all upercase but the little n but i made a mistake and didn't capitilize the RT

58. anonymous

But was i right?

59. anonymous

Zed, im going to do yours now.

60. anonymous

yes you were right and that was the ideal gas law by the way

61. anonymous

Oh, that was a ^3! Divide both sides with (pi)r^2 getting V/(pi)r=4/3r, am i right sofar?

62. anonymous

What does the law state?

63. anonymous

okay so first step is to get r^3 by itself. what do you get?

64. anonymous
65. anonymous

Wait. I take back my first answer. First you divide both sides by 4/3(pi) to isolate r^3

66. anonymous

good. have you done powers before and their inverses?

67. anonymous

I think so, what do you mean?

68. anonymous

okay so we have $r^3=\frac{3V}{4}$ how do I get rid of the cubed part?

69. anonymous

Oh, i have done powers but i dont recall doing inverses, is that like squareroot and cubicroot? I guess we need to get the "cubicalroot" out of r^3.

70. anonymous

We should be able to just divide r by r 2 times.

71. anonymous

3* and by itself i mean the root.

72. anonymous

not quite see let's try this example to help explain it $x^2=4$$x=\sqrt{4}$$x=4^{\frac{1}{2}}$$x=2$

73. anonymous

What? Can you explain that?

74. anonymous

okay so when we bring powers (eg 3) over the equation sign they turn to 1/powers (eg 1/3). if we look at squared when we bring it over it turns to 1/2 which is also known as the square root.

75. anonymous

Why does it become 1/2?

76. anonymous

the may be abit hard to follow but this is why. Let f(x)=y $y=x^7$ $\ln y=7 \ln x$ $lnx=(lny)/7$ $x=e^{(lny)/7}$ $Inverse = f^{-1}(x)=e^{(lnx)/7}$ $f^{-1}(x)=e^{lnx^\frac{1}{7}}$$=x^\frac{1}{7}$

77. anonymous

Now usually when learning this we just accept this as fact that $x^n=x^{\frac{1}{n}}$ where n is a positive integer

78. anonymous

That was probably way too much information at once just use the rule in the above post and try to solve $r^3=\frac{3V}{4}$

79. anonymous

So if r^2 becomes 1/2, then r^3 should become 1/3, right?

80. anonymous

Correct

81. anonymous

That means that i have to maake r^3 to 1/3 and convert 1/3 to 4/12(to merge it with the right side). i then convert the right sides fractions too, getting 9V/12. Now i should be able to merge them, right? so i get r=13/12?

82. anonymous

I screwed that up right...

83. anonymous

What?

84. anonymous

Sorry we want to raise both sides by the power of (1/3)

85. anonymous

r^1/3=3V^1/3/4?

86. anonymous

so the left hand side will be $(r^3)^{\frac{1}{3}}=r^{\frac{3}{3}}=r^1=r$

87. anonymous

I dont understand.

88. anonymous

okay the right side is good. we have $(\frac{3V}{4})^\frac{1}{3}$

89. anonymous

remember on the left hand side we had r^3 and when raised it to the power of 1/3 the powers need to be multiplied.

90. anonymous

Oh! So its r^3*1/3?

91. anonymous

yes exactly it's one of the rules for powers. here are others if you wanted to learn and practice http://www.math.com/school/subject2/lessons/S2U2L2DP.html

92. anonymous

93. anonymous

yes and that simplifies to r=(3V/4)^1/3

94. anonymous

Oh!

95. anonymous

Well I'm off to sleep. I'll be on tomorrow if you want more examples or help :)

96. anonymous

Thanks for everything!