I have no idea how to do this.

[AntiVirus]

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.

[d&q]

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?

[AntiVirus]

Yeah!!!  Thank you very much!!

[Rule]

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.

[rabbit]

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]

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.

[Rule]

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]

I knew six was probably *the* answer that he was looking for. How did I know? Because I look good.

[Chavo]

Or maybe because logic classes don't have any use for negative bases