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#326 Re: Help Me ! » Plzplzplzplz help me with these problems! » 2006-07-23 01:46:22
....One day...ONE DAY, I will help those who need help !
Promise???
Q3:
x+y=1
x^3+y^3=31
Now
(x+y)^3=1=x^3+3x^2y+3xy^2+y^3=
=(x^3+y^3)+3xy(x+y)=31+3xy.1, so
3xy+31=1
3xy=-30
xy=-10,
Now, by x+y=1, we have y=1-x:
x(1-x)=-10
x1=(1-√41)/2
y1=1-x1
x2=(1+√41)/2
y2=1-x2
Q4:
#327 Re: Help Me ! » solving exponents manually » 2006-07-23 01:35:56
Sorry Patrick.
You mean the definition of exponent?
If b is a positive integer integer, then
a^b=a.a.a.a. ... .a --->b times
For example a^1=a; a^2=a.a; a^3=a.a.a
By definition a^0=1;
If b is negative, we use:
#328 Re: Help Me ! » solving exponents manually » 2006-07-23 01:32:11
I have a question.. Do you know what
means? If you do, I can't see how you can have problems calculating it manually.
But he is talking about 2^59, which is much more hard to compute.
Here is it:
2^59=576460752303423488
2^-59=1/(2^59)≈ 1.734723475976807094411924481391906738281e-18
#329 Re: Help Me ! » solving exponents manually » 2006-07-23 01:27:22
aha!
I don't know any method. (which gives exact)
#330 Re: Help Me ! » formula or solution to solve this problem. » 2006-07-23 00:57:43
luca, I think you are getting 55 minutes, because you're losing too much presicion by this 10^16.
Pure symbolic answer is cutter.
#331 Re: Help Me ! » formula or solution to solve this problem. » 2006-07-23 00:36:55
No!
Can't be 55 minutes.
Let
We don't need the exact value of a:
The volume of the glass is r(60), e.a.
Then
Now, by just solving r(x)=V/2 by x, we'll get the answer:
So x is very close to 59 and bigger from 59:
#332 Re: Help Me ! » solving exponents manually » 2006-07-23 00:27:11
please give some example.
#333 Re: Help Me ! » solving exponents manually » 2006-07-23 00:26:11
What does "exponents" mean at all?
If it's a^x=b, then x=ln(b)/ln(a)
#334 Re: Help Me ! » formula or solution to solve this problem. » 2006-07-22 23:38:44
I think you are asking me.
First, MathsIsFun-perfect explanation.
Second- I'm actually not getting v at all. I'm assuming that the glass fills with v drops, so v/2 drops will be needed to full the half of the glass.
#336 Re: Help Me ! » formula or solution to solve this problem. » 2006-07-22 22:46:07
The answer must be>59 minutes, because in the beginning of the 60th minute in the glass will be
(v-1)/2 drops, where v is the number of drops, which full the glass
If you use that the number of drops, falled to the t-th minute (including the t-th minute) is:
so
we know by definition that a(60)=v, so a(59)=v/2-1/2, which is with 1/2 drop smaller from the half of the glass.
#337 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2006-07-22 22:25:17
#k+110
Let
n+3=x^3;
2n+3=y^3
Then
n=x^3-3;
2(x^3-3)+3=y^3
2x^3-3=y^3
The solutions of this diophantine equations are (1,-1) and (4,5)
So we have n=-2 and n=61.
#338 Re: Help Me ! » formula or solution to solve this problem. » 2006-07-22 22:07:33
59 minutes
#339 Re: Introductions » Greetings To All » 2006-07-22 21:41:24
Hi Daset.
#340 Re: Introductions » Um, I'm ben (I think) » 2006-07-22 21:39:41
Hi.
set theory, group theory, vector spaces, topology - not for me.
But see you.
#341 Re: Help Me ! » integrating sqrt(1-x^2) » 2006-07-22 21:29:32
#342 Re: Help Me ! » Logarithm troubles, Need help quick! » 2006-07-22 21:23:41
2. Express 1+ln as a single logaritm.
I think it's
so
#343 Re: Help Me ! » Infinite lightbulb. » 2006-07-22 21:07:15
Very interesting question about the infinity.
My opinion is that infinity is not a number, so it can't be even or odd.
It doesn't have (even or odd) property.
An illustration of what happens:
#344 Re: Help Me ! » Wanted ... a function » 2006-07-22 19:52:45
f(n+1)= nf(n)+f(n-1)
f(n+2)= (n+1) f(n+1)+ f(n)
= ((n+1)n+1) f(n)+ (n+1) f(n-1)f(n+3)= (n+2) f(n+2) +f(n+1)
= ... I don't want to write it out
It will go bigger and bigger, besause in the expansion of f(x) there are 2 f-s.
You will get something as a Fibbonacci tree.
I'm starting to think that there won't be a simple function with this property. What about an integral?
#345 Re: Help Me ! » 2+2 = 3.99 recurring?? » 2006-07-22 19:45:20
3.99... is a number, like the others, and it has some interestion properties, which allow to "calculate" it:
I'm writing 3.(9) instead of 3.999... , because it doesn't use this "...".
For example:
1.101010(234)=1.101010234234234...,
Call 3.(9) C:
C=3.(9)
Now C has an infinite number of digits, but it also have a property, given with the definition:
C 10^n has the same fractional part as C, so we may exclude it, by substracting:
For example:
10C-C=39.(9)-3.(9)=36.(0)=36
C=36/9=4.
That kind of method is used for evaluating different kinds of numbers:
For example
#346 Re: This is Cool » pi and other numbers with infinite numbers of decimals » 2006-07-22 13:00:02
But, just because the pattern is unrecognizable, we can't be sure that every number will appear only finite number of times.
I'm sure that every numbers occur infinitely, but there's a problem - this must be proved to be true.
#347 Re: Help Me ! » the area of the square and rectangle » 2006-07-22 12:11:35
You want pictures?
Here:
#348 Re: Help Me ! » Wanted ... a function » 2006-07-22 10:31:36
f(k)=k for k>=0?
But then f(3)=3f(2)+1=7...
#349 Re: This is Cool » pi and other numbers with infinite numbers of decimals » 2006-07-22 05:34:35
I'm talking about the randomination of the numbers (for example pi).
Numbers in which all the combinations of digits are met, are called normal.
So you're disputing if pi is normal.
It is beleived that it is, but it's not proved.
#350 Re: Help Me ! » the area of the square and rectangle » 2006-07-22 05:27:36
Sorry. I use S for the area.
And tha angle between two straight lines is the smaller of the two (i think...).