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#4126 Re: Help Me ! » Rolling Dice » 2007-02-27 04:52:55
It is quite a hard problem in general though, it's just that for the particular case of you only looking for one 6 you can look for the complement probability instead, which is much easier to find.
If you wanted to know how likely it was to get 2, 3, or even k sixes with m dice, then the problem becomes substantially trickier.
Actually, its a binomial distribution. The probability of getting exactly k sixes (k = 0, 1, m) is
To find the probability of getting at least k sixes, just sum the probabilities for k, k+1, m OR find the probability of getting fewer than k sixes and subtract from 1 (depending on the value of k one would be easier than the other).
#4127 Re: Help Me ! » help with quadratic sequences please. » 2007-02-27 03:13:38
Yes, its cubic. Ive just worked it out. 
#4128 Re: Jai Ganesh's Puzzles » Oral puzzles » 2007-02-26 16:16:43
#4129 Re: Dark Discussions at Cafe Infinity » Optical Illusions, et al » 2007-02-26 15:49:55
How many people? 12 or 13?
#4130 Re: Help Me ! » LaTeX - A Crash Course » 2007-02-26 14:53:42
Latex is getting more and more complex.
Indeed.
#4131 Re: Help Me ! » provement » 2007-02-26 14:38:16
In the picture you can see how the above equality is not true for all x.
You can try it on your calc and check the values of LHS and RHS.
If you square both sides, I think it will be true for all x. 
To i love chem:
#4132 Re: Help Me ! » 2nd deriv of circle versus parabola » 2007-02-26 14:21:15
Thats right, a straight line has zero curvature. In other words, a straight line does not curve!
#4133 Re: Help Me ! » 2nd deriv of circle versus parabola » 2007-02-26 10:24:36
tiny error, I actually was getting minus one over r, positive 1/r.
I was so elated how it was cancelling out, I forgot the minus sign.
But while reading on the subject, I see if it curves clockwise, it's minus.
And counter-clockwise is positive.
Yes, the sign of
depends of that of the second derivative (with respect to x). For the circle, this is positive below the horizontal axis and negative above it (i.e. the tangent is increasing on the lower semicircle and decreasing on the upper semicircle).If you like, you can consider the related concept of radius of curvature instead. This is defined as the reciprocal of the absolute value of
and will always be positive.#4134 Re: Help Me ! » solve it please » 2007-02-26 06:07:37
By inspection,
200 = 2[sup]3[/sup]·5[sup]2[/sup]
500 = 2[sup]2[/sup]·5[sup]3[/sup]
But all right, lets do it systematically
Taking logarithm on both sides (the log can be to any base; here log[sub]10[/sub] will be fine), you get
Now solve for x and y.
#4135 Re: Help Me ! » solve it please » 2007-02-26 05:50:38
By inspection, x = 3, y = 2. (Factorize 200 and 500.) 
Well, these particular equations happen to be easily solvable by inspection, but in general, you can take logarithms for such equations. They will then be converted into simultaneous linear equations, which should be easier to solve.
#4136 Re: Help Me ! » 2nd deriv of circle versus parabola » 2007-02-26 03:12:04
Hey, I didnt think of polar co-ordinates! Thats neat. 
#4137 Re: Help Me ! » 2nd deriv of circle versus parabola » 2007-02-25 17:46:17
Well, actually curvature is defined as
where ψ is the angle the tangent makes with the x-axis (i.e. tan ψ = dy/dx) and s is the arc length of the curve. In other words, curvature is the rate of change of the direction of the tangent with respect to arc length.
On the other hand, the second derivative is rate of change of the tangent itself (i.e. dy/dx) with respect to x. Hence the two are different. Hope this makes sense. 
#4138 Re: Puzzles and Games » Word puzzles » 2007-02-25 13:25:05
Well, it's a difficult one, so if you give up .
Im sorry that one was so hard. 
This one will be slightly easier, I promise.
10. Give an English word that contains the vowels UAEIO in that order (each vowel exactly once).
#4139 Re: Help Me ! » 2nd deriv of circle versus parabola » 2007-02-25 12:51:36
The second derivative does not describe the curvature of a curve; rather it describes the rate of at which the tangent to the curve is changing with respect to the x-axis.
The concept of curvature is different: it is defined as
Yes, a circle does have a constant* curvature (
) equal to the reciprocal of its radius. A circle, however, does not have a constant second derivative.*Constant apart from sign.
#4140 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-25 02:42:20
Maybe its just a flaw in the notation used to write down real numbers? The flaw is that any real number with a terminating decimal (except 0) can be written in two different ways in the notation: e.g. 1 = 1.0000 = 0.9999 , 1.234 = 1.2340000 = 1.2339999 , etc. Its all too easy to be fooled into thinking that two different ways of representing something must mean two different things.
Maybe we should switch to a better notation for real numbers, one in which every real number would have its own unique representation. (Continued fractions, perhaps?) Then the mind would not be fooled into looking for nonexistent infiinitesimal differences between numbers from the way they appear when written down.
Just my tuppenceworth.
#4141 Re: This is Cool » The mathematics of mosques » 2007-02-24 15:12:03
Islamic religion forbids the depiction of living creatures in art. Therefore Islamic artists have had to concentrate on other forms of artistic expression such as calligraphy and abstract shapes hence the diverse and intricate patterns you see in Islamic art. 
#4142 Re: Puzzles and Games » Spot the error » 2007-02-24 09:47:55
Well, Drosss problem is more to do with physics than mathematics, Id say. 
The mistake is in assuming that the ladder always makes a right-angled triangle with the wall and floor. This is true when the ladder is stationary, but when you pull the base away from the wall, the top of the ladder is going to be pulled away as well. Then the Pythagorean relation between
#4143 Re: Puzzles and Games » Word puzzles » 2007-02-24 08:24:56
Well, heres a hint (for the word I have in mind): its relevant to maths. 
#4144 Re: Puzzles and Games » let the magician read your mind » 2007-02-24 08:09:32
Choose a four didgit number write that number backwards divide the smaller number by the larger number, keep your answer
I think you made a mistake I think you mean subtract the smaller number from the larger number. Also, I think the digits of the number must not all be the same (i.e. it must not be 1111, 2222, etc).
#4145 Re: Puzzles and Games » Word puzzles » 2007-02-24 07:11:38
9. Give an English word that contains the vowels UIEAO in that order (each vowel exactly once).
#4146 Re: Introductions » Introducing myself » 2007-02-24 03:51:07
Wow, Ive never felt so welcomed in my life! Thank you all so much!
And Zach
mathematics often gives me insomnia. 
But I love and enjoy it.
#4147 Re: This is Cool » all numbers are equal » 2007-02-24 02:55:13
#4149 Re: Jai Ganesh's Puzzles » 10 second questions » 2007-02-23 12:54:41
#4150 Re: Introductions » Introducing myself » 2007-02-23 12:19:42
Thanks, MathsIsFun and power man!
I live in England. I merely name myself after my favourite character in Jane Austens Emma. 