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#2 Re: Help Me ! » Solve this differential equation » 2014-07-31 03:41:26

Write the equation as

and use the substitution

#3 Re: Help Me ! » Challenging Applied maths question projectiles » 2014-07-27 00:47:32

Just solved it! big_smile


In solving algebraically for
you need to take the minus sign in front of the square root:



This value of
will work. In other words the bullet hits the plane on the way up rather than on the way down.

The computation is straightforward but tricky. You just need to take extra care not to make any careless mistake. smile

#4 Re: Help Me ! » Challenging Applied maths question projectiles » 2014-07-27 00:25:43

When the shot is fired, the plane has travelled a horizontal distance
. (You can picture this by drawing a diagram.)

The time taken for the bullet to rise to height
is given by



I think the idea is to solve for
algebraically and show that
(horizontal distance travelled by bullet)
(distance travelled by plane after passing gun).

#5 Re: Help Me ! » Unit circle / Geometry » 2014-07-25 22:07:49

It’s a unit circle so its radius is 1.

#6 Re: Puzzles and Games » problem on trains » 2014-07-25 21:48:12

Let the length of the train (in km) be
.

Let the speed (in kph) of the train relative to the first person be
; then its speed relative to the second person is
.

Therefore:

Hence:

So the train’s length is 0.05 km – i.e. 50 m.

#8 Re: Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-14 01:38:34

Germany 1-0 Argentina after extra time. Well done Germany! cool

#9 Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-08 22:43:37

Nehushtan
Replies: 14

Germany – out of this world!

Brazil – out of this World Cup …

20140708Brazil1-7Germany.jpg

#10 Re: Help Me ! » Factoring x^3-3x^2+x=0 » 2014-06-30 00:03:16

That’s all you can do. The quadratic polynomial



is irreducible over
and
.

In a way you could write

but this is probably not what you want.

#11 Re: Help Me ! » Sequences » 2014-06-08 00:44:07

Agnishom wrote:

The series is undefined as the first term is
.

#12 Re: Help Me ! » Inequality? » 2014-06-03 10:28:27

Agnishom wrote:

If a,b,c > 0
and abc=1

Prove that a^2 + b^2 + c^2 ≥ a+b+c


Jensen’s inequality states that if
is a convex function then



The function
is convex; therefore



But
by AM–GM.

Hence

#13 Re: Help Me ! » Number Theory » 2014-05-09 08:07:40

Consider

This is a G.P. with common ratio

so we have

But n is odd so

.

Multiplying both sides by

gives

Since the LHS is an integer, the RHS must be an integer. QED.

#14 Re: Dark Discussions at Cafe Infinity » How has mathematics enriched your life? » 2014-05-07 05:18:27

Mathematics has given me a university degree I can wave in front of everyone to show them how smart I am.

#15 Science HQ » Ununseptium » 2014-05-06 04:00:07

Nehushtan
Replies: 2

The periodic table is set to get a new addition – say hello to the superheavy element ununseptium

http://z8.invisionfree.com/DYK/index.ph … p=22021672

#17 Euler Avenue » Why we have 12 and 60 in our time system » 2014-05-03 01:35:15

Nehushtan
Replies: 2

There are 60 seconds in a minute. There are 60 minutes in an hour. And a day has twenty-four hours – 12 hours of daylight and 12 hours night averaged through the year.

What makes the numbers 12 and 60 so special?

http://z8.invisionfree.com/DYK/index.php?showtopic=976

#18 Re: Help Me ! » Set Theory Identity » 2014-05-02 00:28:45

Agnishom wrote:

Please Tell me how I can show


Note that
is a subset of
. In general, if
then
.

Proof:

We must prove that both

and
.

is clear since
is a subset of
.

To prove the other inclusion, suppose

and let
.
. If
we are done. If
then, since
, we have
as well. In either case
. Hence
.

#19 Re: Help Me ! » Set Theory Identity » 2014-05-01 22:52:50

Agnishom wrote:

Sorry, it is supposed to be This:
Prove that:

That’s better. smile

and it is easy to see that

.

#20 Re: Help Me ! » Set Theory Identity » 2014-05-01 22:31:41

Something is wrong with your question.

#24 Re: Help Me ! » How to solve this? » 2014-04-01 02:12:15

Let’s assume

is 1 or prime. Then it divides 2 or
.

(i)

divides 2
or
or
. So
.

(ii)

divides
. For this to be an integer,
. So
. So
which is the same as (i) above.

So

if
is 1 or prime. There are other solutions if
is not 1 and not prime – but as you are not told to find them all, I think I’ll stop here.

#25 Re: Euler Avenue » Contradictory mathematical terminologies? » 2014-03-30 13:13:10

JaneFairfax wrote:

“Contradictory” is perhaps not a good word to use in the title of this thread. “Oxymoronic” might be better, I believe. It is not contradiction that I wish to explore, but rather oxymoron: http://z8.invisionfree.com/DYK/index.php?showtopic=69 big_smile

If I said that someone was an unpleasant kind of person, I would be uttering an oxymoron.

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