Inopeki
ab=c
Solve for a
Do i need to divide both sides by b?
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Zed
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yes
Inopeki
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3
And that is all?
Zed
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yes, so when you do that what will you get?
Inopeki
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3
a=a?
Zed
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1
\[\frac{ab}{b}=\frac{c}{b}\]
\[a=\frac{c}{b}\]
Inopeki
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3
Oh! now i get it, can you set up another example so i can try?
Zed
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1
Sure ax+y=c, solve for x
Inopeki
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3
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
Inopeki
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Is this correct?
Zed
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Really close but we need to either get rid of the y first before divide or also divide the y by a
Inopeki
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3
YES! Thanks for teaching me :)
Inopeki
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3
aw :(
abdul_shabeer
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No, first start by subtracting y from both sides
Inopeki
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3
Alright, so ax+y=c
ax=c-y
x/a=c/a-y
x=c/a-y
Zed
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remeber that when you divide the a you need to do it to all the terms
Inopeki
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Where did you get z?
Inopeki
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Oh right.. so x=c-y/a
zbay
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2
\[x=\frac{c-y}{a}\]
Zed
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zbay is correct
zbay
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Inopeki got the answer i just put it in the equation maker for ease of the viewers
Inopeki
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Yay! :D
Zed
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inopeki you need to write x=(c-y)/a just to make it clearer. i see it now good work
Inopeki
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Thanks for the help :) Is there any way you can make it a little harder to give me a challenge?
zbay
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yea i will come up with one for you
Inopeki
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Thanks.
zbay
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2
\[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]
Solve for T_2
Inopeki
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umm.. ill try
FoolForMath
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Nobody mentioned division by zero ?!!
abdul_shabeer
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Good observation @ Foolformath
Inopeki
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Well to begin with i need to multiply both sides with P2V2, getting P1V1/T1*P2V2, right?\[P _{1}V _{1}divT _{1}+P _{2}V _{2}=T2\]
zbay
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I'll lay it out by steps for you
Inopeki
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3
NOO. wait. Its
abdul_shabeer
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Cross multiplication
Inopeki
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P1V1/T1*P2V2=T2
zbay
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lcd = T_1T_2
\[T_2P_1V_1=V_2P_2T_1\]
\[T_2=\frac{V_2P_2T_1}{P_1V_1}\]
Inopeki
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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.
Inopeki
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3
No?
zbay
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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
Inopeki
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What is an lcd? What makes T1 jump up?
zbay
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lcd= lowest common denominator
Inopeki
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What is that?
Inopeki
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Is a denominator the 1 in T1?
zbay
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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
Inopeki
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Why do we get T1 on both sides of the line?
zbay
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because you are multiplying by t1t2 but on each side one of them will cancell
Inopeki
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Ah
zbay
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Good job that was a hard one
Inopeki
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Thanks, when am i going to get to learn this in school?
Zed
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what grade are you?
Inopeki
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3
8th
zbay
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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.
Inopeki
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Oh, cool. What should i do now?
zbay
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2
PV=nrt solve for n
Zed
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And then try this \[V=\frac{4}{3}\pi r^3\] Solve for r
Inopeki
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Divide both sides by rt, getting PV/rt=n, am i right? By the way, why is PV upper case?
Inopeki
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Zed, isnt that for volúmes of spheres or something? exept r should be ^3
zbay
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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
Inopeki
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But was i right?
Inopeki
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Zed, im going to do yours now.
zbay
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yes you were right and that was the ideal gas law by the way
Inopeki
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Oh, that was a ^3! Divide both sides with (pi)r^2 getting V/(pi)r=4/3r, am i right sofar?
Inopeki
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What does the law state?
Zed
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okay so first step is to get r^3 by itself. what do you get?
Inopeki
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3
Wait. I take back my first answer. First you divide both sides by 4/3(pi) to isolate r^3
Zed
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good. have you done powers before and their inverses?
Inopeki
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I think so, what do you mean?
Zed
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okay so we have \[r^3=\frac{3V}{4}\]
how do I get rid of the cubed part?
Inopeki
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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.
Inopeki
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3
We should be able to just divide r by r 2 times.
Inopeki
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3* and by itself i mean the root.
Zed
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not quite see let's try this example to help explain it
\[x^2=4\]\[x=\sqrt{4}\]\[x=4^{\frac{1}{2}}\]\[x=2\]
Inopeki
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What? Can you explain that?
Zed
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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.
Inopeki
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Why does it become 1/2?
Zed
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the may be abit hard to follow but this is why.
Let f(x)=y
\[y=x^7\]
\[\ln y=7 \ln x\]
\[lnx=(lny)/7\]
\[x=e^{(lny)/7}\]
\[Inverse = f^{-1}(x)=e^{(lnx)/7}\]
\[ f^{-1}(x)=e^{lnx^\frac{1}{7}}\]\[=x^\frac{1}{7}\]
Zed
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Now usually when learning this we just accept this as fact that \[x^n=x^{\frac{1}{n}}\] where n is a positive integer
Zed
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That was probably way too much information at once just use the rule in the above post and try to solve \[r^3=\frac{3V}{4}\]
Inopeki
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3
So if r^2 becomes 1/2, then r^3 should become 1/3, right?
Zed
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Correct
Inopeki
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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?
Inopeki
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I screwed that up right...
Inopeki
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What?
Zed
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Sorry we want to raise both sides by the power of (1/3)
Inopeki
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r^1/3=3V^1/3/4?
Zed
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so the left hand side will be \[(r^3)^{\frac{1}{3}}=r^{\frac{3}{3}}=r^1=r\]
Inopeki
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I dont understand.
Zed
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okay the right side is good. we have \[(\frac{3V}{4})^\frac{1}{3}\]
Zed
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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.
Inopeki
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3
Oh! So its r^3*1/3?
Inopeki
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So the answer is r^3*1/3=3V^3/4
Zed
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yes and that simplifies to r=(3V/4)^1/3
Inopeki
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Oh!
Zed
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Well I'm off to sleep. I'll be on tomorrow if you want more examples or help :)
Inopeki
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Thanks for everything!