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a2 = b2 + c2 - 2bc * cos(θ)
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(A ∧ B) ∨ A

This is equivalent to just 'A', but I can't remember how to simplify that out of it. Hints, please? : )
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If B is true, then the "AND B" is a no-op and you're left with "A OR A" which is just A.
If B is false, then "(A AND B)" is false and "(A AND B) OR" is a no-op, leaving A.

You mean like that? Or is there a specific theorem name you're looking for?
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Well I checked it by exhaustion which is a sufficient proof, but I was looking for an algebraic simplification.
[Edit] Something from http://en.wikipedia.org/wiki/Propositional_calculus#Basic_and_derived_argument_forms can probably do it. Haven't read the whole list yet.
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Since absorption is an axiom, you shouldn't have to prove it symbolically. In fact, I'm not sure you can prove it just using other axioms. A truth table should suffice.
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I was trying to prove to myself that I had rewritten this code
  function futureUnpaidInvoices() : List<AccountInvoice>{
    var invoices = this.InvoicesSortedByDate.where(\ inv -> 
            (
              inv.InvoiceItems.Count > 0 or 
              inv.ManualInvoice
            ) and
            (
              inv.PaidStatus != TC_FULLYPAID and 
              inv.InvoiceItems.Count > 0
            ) and
            (
              !inv.InvoiceItems.hasMatch(\ii->ii.DownPaymentBool)
            )
             
             ).toList()
     return invoices
  }
correctly into this -
  function futureUnpaidInvoices(includeDown : boolean) : List<AccountInvoice>{
    var selectSOMEofTheTHINGS = \ inv:Invoice -> 
            ( inv.InvoiceItems.Count > 0 or inv.ManualInvoice ) and // legit
            ( inv.PaidStatus != TC_FULLYPAID ) and // pending or outstanding
            ( includeDown or !inv.DownPayment ) // no downs unless requested
            
     return this.InvoicesSortedByDate.where(selectSOMEofTheTHINGS).toList()
  }

Turns out my change is correct, so that's nice to see.

It's also nice to find out the reason I couldn't derive the result I wanted was because that transformation is axiomatic. We had what I thought was a pretty good coverage of Boolean algebra in CS301 but I don't remember ever seeing the absorption axiom before. I think I'm going to go read that article in detail.
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Two things.

1. I've seen it explained elsewhere, but not well. Can anyone show the formula for 2+2=5?

2. Another toughie. Can anyone explain 4th dimensional figures. And don't just link to a Wikipedia article, I mean an actual explanation. I'd appreciate it!

Thanks!
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The first is a reference to George Orwell's novel 1984.

I'd need to know exactly what you're referring to with regards to the second if you want an actual answer. Are you interested in contour plots or what? Otherwise, I just suggest you wait until multivariable calculus before you start considering higher dimensions.
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For 2, something along these lines.

Number one I've seen done places. It's weird. I DO know the reference.
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With regards to number one, you've seen it done incorrectly.

Well, with regards to the math, you basically treat it the same way as any number of other dimensions in standard Euclidean space. It doesn't really matter if it's 4 dimensions or 400 dimensions. One's just less work.

As far as expressing a four dimensional object in fewer dimensions, think of a contour plot or topographic map. The image you see is a represntation of it in fewer dimensions. Here's an interactive example.

Basically, the way level sets work is you keep one value constant and then draw what you have from there. So, as you vary one value, the object will appear to be shifting when it is, in fact, not. I'll go see if I can find an interactive example of that. (Note, this doesn't seem to work for me, but it might for you)
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I think I sort of get #2. Thanks.

As for one: http://www.warriorforum.com/off-topic-forum/52565-proof-2-2-5-a.html
That's where I first found it.
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That "proof" isn't even syntactically correct, let alone mathematically correct.
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You can find a slightly better attempt debunked a few threads down, in the "4=5" thread.
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∏=3.141592653589793238462643383279502884197169399375105820974944592307816406286 that's all I know.
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That was incorrect.
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The pi thing? It's correct, isn't it?

EDIT: Unless you mean he/she didn't specify the amount of decimal places and that 22/7 would be a better answer.
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How would I solve Screen shot 2012-03-25 at 2.02.50 PM.png for x?

I've tried it a few times but I can't get the answer which is 3.

The red L is just the question number.
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Multiply both sides by 18. This will eliminate the fractions. From there, distribute the the coefficients into your parenthesized terms. After that you isolate the x onto one side. From there, you just divide out the coefficient.

Hint: You're trying to get to 3.
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Dread said:
The pi thing? It's correct, isn't it?

EDIT: Unless you mean he/she didn't specify the amount of decimal places and that 22/7 would be a better answer.
Pi is not expressible as a decimal number - it can only be approximated.
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@MagicalLegume, cool thanks.
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22/7 is only accurate to two decimal places.
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Wow sorry my 31 on my ACT wasn't good enough for you. I'll have to take it again won't I?
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...What?
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Someone is butt-hurt.
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I'm devastated that I got proven wrong. But whatever you can't be right all the time.
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The Forum > Math & Science > Math Problem Thread
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