Math Is Fun Forum

Of the five numbers considered important in mathematics, this number relates four.
I think this equation was given by Loenard Euler.
This, I think,  is a result of
e^(i*theta) = cos (theta) + i sin(theta)
and
Abraham de Moivre's theorem, according to which
(Cos(theta)+i*sin(theta))^n = cos n(theta) + i*sin n(theta)
which can be written as
e^(n*i*theta) = Cos n(theta) + i*sin n(theta)

Cos(Sin A) is always greater than Sin (Cos A),
as rightly pointed out by Mathsy!
We shall test this for three values in the first quadrant, in degrees.
First, 0.01°.
Cos (Sin A) > Sin(CosA).
Next, for 45°
Again, Cos (Sin A) > Sin(CosA).
Finally, for 89.9°
Yet again, we get the same result.
I shall try to search for a proof, or prove it myself!

We would be missing you two!
Bon Voyage!

....and I heard the refrigerator was a washing machine!

There's a better one! Truly universally acceptable, but not being put into use anywhere (I think! )
1,0000 = Myriad
1,0000,0000 = Myllion
1,0000,0000,0000 = Byllion etc.

1/2
Because there's nothing special about Bill's coin!
Because the probability of getting (head, head and head),
(head, tail, and head) are the same, that is 1/8 !

There are only two:-
9x - 4y = 2,000
7x - 3y = 2,000

Solving for 'x', the annual income of the two can be calculated. They would be 9x and 7x.

#7
The ratio of annual incomes of two persons is 9:7 and the ratio of their annual expenditure is 4:3. Each of them saves $2000 yearly. Find their annual incomes.

31,100 = S - [500+0.04(s-10,000)]
31,100 = S -[500 + 0.04s - 400]
31,100 = S - 100 - 0.04s
31,200 = 0.96 S
S = 31,200 / 0.96
S = 32,500

Problem #6

A salesman's commission is 5% on all sales up to $10,000 and 4% on all sales exceeding this. He remits $31,100 to his parent company after deducting his commission. His sales was worth $_________.

Reminded me of an old joke:-

The European Union commissioners have announced that agreement has been reached to adopt English as the preferred language for European communications, rather than German, which was the other possibility.

As part of the negotiations, Her Majesty's Government conceded that English spelling had some room for improvement and has accepted a five-year phased plan for what will be known as EuroEnglish (Euro for short).

In the first year, 's' will be used instead of the soft 'c'. Sertainly, sivil servants will resieve this news with joy. Also, the hard 'c' will be replaced with 'k.' Not only will this klear up konfusion, but typewriters kan have one less letter.

There will be growing publik enthusiasm in the sekond year, when the troublesome 'ph' will be replaced by 'f'. This will make words like 'fotograf' 20 per sent shorter.

In the third year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible. Governments will enkourage the removal of double letters, which have always ben a deterent to akurate speling. Also, al wil agre that the horible mes of silent 'e's in the languag is disgrasful, and they would go.

By the fourth year, peopl wil be reseptiv to steps such as replasing 'th' by 'z' and 'w' by 'v'.

During ze fifz year, ze unesesary 'o' kan be dropd from vords kontaining 'ou', and similar changes vud of kors; be aplid to ozer kombinations of leters.

After zis fifz yer, ve vil hav a reli sensibl riten styl. Zer vil b no mor trubls or difikultis and evrivun vil find it ezi tu understand ech ozer. Ze drem vil finali kum tru.

You got it √