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#26 Re: Jai Ganesh's Puzzles » 10 second questions » 2011-11-04 15:15:02

ganesh wrote:

#3350. Which is the prime number divisible by

?

I have been reading posts back and forth about this.  This sum,
which is even, does not divide any prime number.

The question could have been "Which prime number divides this sum?"

2 would be an answer.

But, if the question meant was to determine the largest prime
number that divides (into) this sum, then the question stated
should be along the lines of:

"What is the largest prime that divides

#27 Re: Exercises » Is this cool with you? » 2011-11-03 11:24:18

bobbym wrote:

You are welcome and nice to see you are not rusty.

New problem:

Prove:

When n>0

#28 Re: Jai Ganesh's Puzzles » General Quiz » 2011-11-01 05:10:28

ganesh wrote:

This section would contain any question under the sun, sometimes mathematics too!

1. What are Deimos and Phobos?

The answer given is not the only one.  Unless the question is narrowed down,
think

#29 Re: Exercises » What do you think? » 2011-10-31 10:55:34

bobbym wrote:

A new problem:


What is the area of the largest triangle that can fit inside of a square with sides s?
What type of triangle is it?

This is not a proof.  You have to account for the fact
that certain triangles have heights greater than s units.
Then show that, if true, their bases would have to be
too small so that

#30 Re: Exercises » Is this cool with you? » 2011-10-30 16:41:55

#31 Re: Exercises » Is this cool with you? » 2011-10-30 07:31:09

The answer to the exercise in post #1109 still has not been posted.

#32 Re: Help Me ! » Math induction » 2011-10-26 14:28:14

JohnJ wrote:

Hi folks,

Gotta solve this one as well. Any help appreciated.

For which non-negative integers is

n² ≤ n! 
?

Answer to be proven with math induction.

regards

John J

User TheDude, there is a factorial sign in that exercise.

#33 Exercises » Sums of series with odd positive denominators » 2011-10-25 07:15:38

#34 Re: Exercises » Proving the divergence of the Harmonic series (alternate method(s)) » 2011-10-20 10:59:13

Another way:


Assume S is a finite sum.


Group it as:


S = 1 + [(1/2 + 1/3 + 1/4) + (1/5 + 1/6 + 1/7) + (1/8 + 1/9 + 1/10) + ...] > **


1 + [3(1/3) + 3(1/6) + 3(1/9) + ...] =


1 + [1 + 1/2 + 1/3 + ...] =


1 + S


But this has S > 1 + S.


This is impossible if S is to have a finite value.

So this is a contradiction, and therefore S must
not have a finite sum.

That is, S is divergent.


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#35 Re: Help Me ! » volume of a cone » 2011-10-15 17:28:51

Joel wrote:

Can anyone help me, how to derive the formula of the volume of the cone 1/3*pi*r^2*h ?


The volume of a right circular cone with radius r and height h, equals the
area of the right triangle (let the base = r and the height = h), which is
being revolved along the line containing the line segment h, multiplied by the
circumference using the r/3 part of the centroid* as the radius of revolution.

The centroid of a triangle is where all of its medians intersect.
The centroid is the geometric center of the triangle.**

Then the formula for the volume is

the area of the triangle, multiplied by the circumference at the
geometric center (centroid), and using r/3 as the radius of revolution. 
This is:





- -  . . - - . . - - . . - -  . . - - . . - - . . - - . . - -




* Suppose a right triangle is situated on the xy-plane with the
radius extending from (0, 0) to (r, 0) and the height extending
from (0, 0) to (0, h).


The x-coordinate of this centroid is r/3.  (This can be worked out using
coordinate geometry.)


** Source:
http://en.wikipedia.org/wiki/Centroid

#36 Re: Help Me ! » Geometry; Quadrilateral; Midpoints » 2011-10-15 15:31:43

Agnishom & reconsideryouranswer edit wrote:

A quadrilateral PQRS  has angular bisectors of angle S
and angle P which meet inside the quadrilateral at a point O.

Does the measure of angle Q + the measure of angle P =
twice the measure of angle SOP?

No other clues are visible

For instance, it *does* work for a quadrilateral when it is a square.

However, I am looking for a counterexample with the following:


#37 Re: Exercises » Proving the divergence of the Harmonic series (alternate method(s)) » 2011-10-15 14:20:21

I will start with:


Again, assume S is a finite sum.


S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...


S = 1 + (1/2 + 1/3) + (1/4 + 1/5) + (1/6 + 1/7) + (1/8 + 1/9) + ...


S = 1 + (5/6) + (9/20) + (13/42) + (17/72) + ...


#38 Re: Puzzles and Games » Clock puzzlers » 2011-10-15 06:50:11

bobbym wrote:

Hi Darby;

I am sorry but I have been unable to find anything for those
that does not use something more complicated then what
you have been using.

10:38

1 = [0(3 + 8)]!


- - - - - - - - - -- -


10:47

1 = [0(4 + 7)]!


- - - - - - - - - - -


10:57

1 = [0(5 + 7)]!


- - - - - - - - - - -


10:58

1 = [0(5 + 8)]!


- - - - - - - - - -


10:59

1 = [0(5 + 9)]!

__________________





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#39 Re: Puzzles and Games » Clock puzzlers » 2011-10-14 20:15:58

Darby wrote:

1 = (0 X 2 X 7)!

1 = (0/2 X 7)!

1 = [0 X (2 + 7)]!

1 = [0 X (2 - 7)]!

1 = [0 X 2^7]!

1 = [0/(2^7)]!

1 = (0^27)!

1 = [0^ (2 X 7)]!

1 = [0^(2^7)]!

1 = [(0^2)^7]!

1 = [0^2 X 7]!

1 = [0^(2/7)]!

1 = [(0/2)/7]!

1 = [(0 X 2)/7]!

1 = (0/2/7)!

1 = (0/2 X 7)!

1 = (0/27)!

1 = [0/(2 X 7)]!

1 = [(0 X 2)^7]!

1 = [(0/2)^7]!

1 = [0/(2^7)]!

1 = [0/(2 + 7)]!

#40 Re: Help Me ! » 3.3333333 + 6.66666666 » 2011-10-11 05:12:23

bob bundy wrote:

.

It need not be a person.  Certain animals have a concept of numbers and counting.
And numbers, (counting numbers, for instance) have their own existence independent
of human thought.  Before there were humans to think about numbers,
there were always places where there was one thing, two things, etc.

That's very interesting.  If it's true, I don't think it changes my argument;
just substitute 'some animals including humans' for 'person'.

But which animals did you have in mind?

Certain chimpanzees

----------------------------------------------


#41 Re: Help Me ! » 3.3333333 + 6.66666666 » 2011-10-10 18:05:18

bob bundy wrote:

but three doesn’t exist except in the mind of a mathematically inclined person.

It need not be a person.  Certain animals have a concept of numbers and counting.
And numbers, (counting numbers, for instance) have their own existence independent
of human thought.  Before there were humans to think about numbers,
there were always places where there was one thing, two things, etc.

bob bundy wrote:

So, in certain circumstances, it’s ok to say 3 + 4 = 7. 

But, notice this rule doesn’t always work. If I walk 3 miles and then walk 4 miles,
I'm not necessarily 7 miles away from where I started.

This is not a correct example of "a rule that doesn't always work,"
as you put it.  You're comparing apples and oranges.  Those movements equal
a total of 7 miles walked.  The rule works.  Mixing in where someone ended
up relative to the starting point is changing the subject.
 

bob bundy wrote:

So, for instance, when we make the rule for powers:

we find it works ok with all the other stuff we know about powers.

Then when someone poses the question “I wonder if we can find a sensible meaning for:

the answer is, yes, we can.  It makes good sense to let it have the value ‘1’ because this
is consistent with the rule of powers:

You have made a blanket statement.  It is not so where x = 0.


Under that method,


So 0^0  could  equal 1,



#42 Re: Exercises » Proving the divergence of the Harmonic series (alternate method(s)) » 2011-10-10 02:05:28

I want everyone to see this, so I did not hide it:


Prove that the Harmonic series is divergent.


Let S = the Harmonic series.

Assume S has a finite value.


S = 1  + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ...



S = (1 + 1/2) + (1/3 + 1/4) + (1/5 + 1/6) + ...


> (2/2) + (2/4) + (2/6) + ...


= 1 + 1/2 + 1/3 + ...

= S


But this states that S > S, which is impossible,
because S is assumed to be finite.

So, this is a contradiction, and the Harmonic series
is divergent.

#43 Exercises » Proving the divergence of the Harmonic series (alternate method(s)) » 2011-10-09 06:12:29

Without using either of the two specific methods shown at this
Wikipedia site (in the top first few pages), use an alternate
method to prove the divergence of the Harmonic series:


http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)

#44 Re: Dark Discussions at Cafe Infinity » How long ago was thor around, according to myth? » 2011-10-08 15:45:32

LQ wrote:

How long ago was

thor
around, according to myth?

Is it really only 300 years ago?

LQ,

"Thor" is a proper noun, so it is capitalized.

#45 Re: Puzzles and Games » The Monty Hall Problem » 2011-10-07 07:06:44

This game assumes that the car is the prize and the goat
is not.  If I were a young child playing it, I wouldn't switch
if I already had the goat in view, because I like goats,
and I would have no use for a car.

#46 Re: Help Me ! » 3.3333333 + 6.66666666 » 2011-10-07 06:59:51

anonimnystefy wrote:

look at it this way: 0,5 is just another way of representing 1/2,and by the same logic 0,3333... recurring is just another way of representing as 1/3.

Also, don't forget to include that

#47 Re: Help Me ! » Calculus » 2011-09-30 16:05:45

IMMORTALX,

post all of your work/attempts at the problems
first so that you may be helped where you are
stuck.  Your input is needed, and none of the
answers on any of your threads should just be
delivered to you.  We're to be coaches, and
you're to be the athlete who does the work/practice
so you can be guided in a better direction.

#48 Re: Help Me ! » Calculus Find y'' by implicit differentiation » 2011-09-30 16:02:27

IMMORTALX,

post your work/attempts first so that you may be
helped with where you are stuck.

#49 Re: Help Me ! » Calculus: Find dy/dx by implicit differentiation » 2011-09-30 16:01:02

IMMORTALX,

post your work/attempts first so you may be helped
with where you are stuck.

#50 Re: Help Me ! » Calculus: Find the derivative of the function. » 2011-09-30 15:59:33

IMMORTALX,

you have to post your work thus far (your attempts),
so that you can be helped.  Show us where you are
stuck by showing your work . . . first.

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