### Author Topic: I have no idea how to do this.  (Read 1933 times)

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#### AntiVirus

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##### I have no idea how to do this.
« on: August 24, 2006, 05:50:42 PM »
Determine the base r of a number system such that 225(r) = 89(10).

Okay, the r and 10 are subscripts and the = sign in my book actually has three lines as oppose to two.  I don't know how to do that on these forums, so sorry about that.  Anyway, does anyone know how to figure out the number system 225 is in?

Ich habe nicht idee.
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Aforetime crowned by lilac and lily,
Lay now forevermore slender;
And all winds that liven
Silhouette a lone existence;
A leafless oak grasping at eternity.

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#### d&q

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##### Re: I have no idea how to do this.
« Reply #1 on: August 24, 2006, 06:06:30 PM »
It is in base 6. How you do it is, first, you know that in each place there is:

2   2  5

r^2 r^1 r^0

2(r^2) is less than 89, so you know that has to be less than 7, since 2(7^2) = 98. So I just sexually chose 6.

2      2      5
2(6^2) 2(6^1) 5(6^0)

This works out to 72, 12, and 5.

72 + 12 + 5 = 89.

I hope I was understandable?
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#### AntiVirus

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##### Re: I have no idea how to do this.
« Reply #2 on: August 24, 2006, 06:28:32 PM »
Yeah!!!  Thank you very much!!
The once grove of splendor,
Aforetime crowned by lilac and lily,
Lay now forevermore slender;
And all winds that liven
Silhouette a lone existence;
A leafless oak grasping at eternity.

"They say that I must learn to kill before I can feel safe, but I rather kill myself then turn into their slave."
- The Rasmus

#### Rule

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##### Re: I have no idea how to do this.
« Reply #3 on: August 24, 2006, 10:56:27 PM »
I think it's best to approach this problem more generally.  Your method is ok since you verify your guess, but it wouldn't be too useful in a situation where the base is something like 6.1, and it can lead to carelessness as it did in this thread (resulting in an incomplete solution)!

Solve the polynomial
2r^2 + 2r + 5 = 89

2r^2 + 2r - 84 = 0

6 is a solution, but now we also see that -7 is!

(P.S. The three bars equals means, "is logically equivalent to" or "by definition." In most cases, like here for example, it's effectively the same as a regular equals.  The three bars equals can almost* always be replaced by a regular equals, but the reverse cannot be done so often without making a few additional notes.  For example, if you are calculating the time it takes for someone to run 10km at 15 km/hr, it wouldn't make sense to say the t (triple equals) 2/3hr, unless you clearly defined t using the given conditions, since time in general won't equal 2/3.)

*I'm covering myself incase someone decides to be exceedingly pedantic.

« Last Edit: August 24, 2006, 11:10:50 PM by Rule »

#### rabbit

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##### Re: I have no idea how to do this.
« Reply #4 on: August 25, 2006, 09:33:42 AM »
The triple bars is "numerically congruent to" and is used to equate numbers in different bases, modulo, etc...  It's essentially "equals" for more abstract mathematics, but it does take on other properties too (which I forget).

#### d&q

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##### Re: I have no idea how to do this.
« Reply #5 on: August 25, 2006, 06:56:07 PM »
I think it's best to approach this problem more generally.  Your method is ok since you verify your guess, but it wouldn't be too useful in a situation where the base is something like 6.1, and it can lead to carelessness as it did in this thread (resulting in an incomplete solution)!

Solve the polynomial
2r^2 + 2r + 5 = 89

2r^2 + 2r - 84 = 0

6 is a solution, but now we also see that -7 is!

I was aware of that method, but I just randomly happened to know that six was the answer from looking at it, so I kinda just worked backwards to prove it was six, instead of trying to solve the problem that way.
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#### Rule

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##### Re: I have no idea how to do this.
« Reply #6 on: August 25, 2006, 07:00:36 PM »
I think it's best to approach this problem more generally.  Your method is ok since you verify your guess, but it wouldn't be too useful in a situation where the base is something like 6.1, and it can lead to carelessness as it did in this thread (resulting in an incomplete solution)!

Solve the polynomial
2r^2 + 2r + 5 = 89

2r^2 + 2r - 84 = 0

6 is a solution, but now we also see that -7 is!

I was aware of that method, but I just randomly happened to know that six was the answer from looking at it, so I kinda just worked backwards to prove it was six, instead of trying to solve the problem that way.

If you knew that the solution could involve solving a quadratic equation, you should have known that 6 was only *an* answer, not *the* answer.

1/2 marks.

#### d&q

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##### Re: I have no idea how to do this.
« Reply #7 on: August 25, 2006, 07:02:58 PM »
I knew six was probably *the* answer that he was looking for. How did I know? Because I look good.
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#### Chavo

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##### Re: I have no idea how to do this.
« Reply #8 on: October 25, 2006, 09:45:25 AM »
Or maybe because logic classes don't have any use for negative bases