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Which is greater?
Cos (Sin A) or Sin (Cos A)?
....and I heard the refrigerator was a washing machine! ![]()
Hi, I love pi! Welcome to the forum!
Trying to find the square root of 0 using logarithms is not possible
as log 0 is not defnined. This is because any number raised to any number cannot be 0. That includes 0.
The square root, cube root, fourth root etc, of 0 IS 0.
This is because
0² = 0
0³ = 0
0^4 = 0 and so on.
Any nth root of 0 is 0, the only condition being n ≠ 0.
This follows from the fact that
if a^b = c, then bth root of c = a.
The birth of imaginary numbers is, indeed, interesting.
I had read somewhere that imaginary numbers have practical applications too!
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.
My favourite is the one with the square made up of a slightly smaller square and 4 right-angled triangles.
And thats the only one I remember! ![]()
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 !
I would be wasting close to 33 years of my life if i did (the American Billion), assuming I don't sleep!
Wow, four simultaneous equations...
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. ![]()
There are two types of decimals:- Terminating and recurring.
A number like 12.5 or 1.25 or 3.75 is a terminating decimal.
On the other hand, sometimes, you have numbers like 0.33333333333333.................,
0.166666666666.....................,
1.6666666666666 etc which are called recurring decimals.
For example, 1'/2 or 1/8 is a terminating decimal.
1/3, 5/6 etc are recurring decimals.
I was talking about how recurring decimals are convereted into rational numbers (that is, fractions).
If that is clear, look at the following illustration.
How do we convert 2.166666666666.............. into a rational number?
Let x = 2.16666666666666666............
10 x = 21.66666666666666666.......... ----------(I)
100x = 216.6666666666666666......... ----------(II)
Subtracting (I) from (II),
90x = 195,
x = 195/90 or 13/6.
Now, have I made myself clear?
#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.
As simple as that!
But you would have to remember
(1) A second is a billion (US) nanoseconds but not a billion (UK) nanoseconds.
and
(2) An American Gallon is different from a gallon in UK
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 ![]()
There once was a person called Mathsy...
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 $_________.
Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival? ![]()
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'd kill me for telling this, but the solution is
that he was born in a hospital in room No.1975
and he died in a hospital in room No.1995.
I never said those were the years, did I? ![]()
You got it √
A cistern can be filled by two pipes A and B separately in 45 minutes and 36 minutes respectively. A tap C at the bottom can empty the cistern in 30 minutes. If the tap C is opened 7 minutes after the two pipes A and B are opened, in how many minutes will the cistern be full?
A person was born in 1975 and he died in 1995. He was 25 years of age when he died. How?
(This one's a lateral thinking puzzle
)
1 20 19
2 19 17
3 18 15
4 17 13
5 16 11
6 15 9
7 14 7
8 13 5
9 12 3
10 11 1
That's 100!
Re-arranging,
1 17 16
2 20 18
3 13 10
4 19 15
5 16 11
6 18 12
7 15 8
8 14 6
9 11 2
10 12 2
100 yet again!
Should it be always (n/2)² for 0 to n??? ![]()
(Just like the side total of a magic square containing numbers 1 to n² is
(n³+n)/2 ???
)
I once knew someone named justlooking,
Who had a knack for hookin'
Everytime he tried his skill
I um unable to reply. I shall wait for your post and comment on that later, MathsIsFun.
#4 (Without paper, pencil; Time limit : 1 minute)
The sum of three numbers is 174. The ratio of the second number to the third is 9:16 and the ratio of the first number to the third is 1:4. The second number is _______.
Since both the ratios have 4 or a multiple of 4 for C,
the ratio A:B:C = 4:9:16.
The sum of these is 29, and it can be noticed 174 is 29 x 6.
Therefore, the second number is 9 x 6, that is 54.
Ist truck:- 3 full cylinders, 1 half-full and 3 empty
IInd truck:- 2 full cylinders, 3 half-full and 2 empty
IIIrd truck:- 2 full cylinders, 3 half-full and 2 empty
PS:- The Moderator may remove my reply if he/she wants it to be left open.
You are right, Mathsy! ![]()
#4 (Without paper, pencil; Time limit : 1 minute)
The sum of three numbers is 174. The ratio of the second number to the third is 9:16 and the ratio of the first number to the third is 1:4. The second number is _______.