All Answers 358098 Answers

The area is given by....

A = (1/2) r^2 (Θ )         where A is the area and Θ is the radian measure if the arc....so we have

A = (1/2) 6^2 * (pi / 4)  =   36 pi /  8   =  about 14.14 cm^2

There's an easily-remembered "conversion"  to figure out a car's rate per second or its mph...

60mph  = 88 ft per second

So.....put the thing we're looking for on "top" of the same quantity in the conversion and multiply by the other side......thusly.....

[70/60 ] x 88 = 102.66  ft/s

I did this one (after a bit of "fumbling') in a slightly different manner...but...the results are really close to yours!!

I noted that the minute hand moves through 6° in  a minute.....and I noted that the hour hand moves through (1/2)° every minute....so....

At 6:30PM, for instance.....the hour hand is 15°  ahead of the minute hand. So it will take the minute hand....

(6 - 1/2)T  = 15  .....T = about 2.727272727272727 min = 2 min 43.636363636363638 seconds to "catch up" to the hour hand  ..i.e.  the hands are "even' at  about  6:32:43AM

 So....solving the following "formulas" for the times between the hours when the hands are in the same position, we have

7 - 8   (5.5)T = 45    ...T = 8.1818181818181818 minutes afte 7:30AM  = about  7:38:11

8 - 9    (5.5)T = 75   ....T = 13.6363636363636364 mintes after 8:30AM  = about 8:43:38

And from here, I noted that each successive time would be (about) 1hr 5 min 27 seconds later than the previous one giving the remaining two times of ....   9:49:05AM and 10:54:32AM

And the hands don't cross again until noon.

The situation existing after 1PM is similar......

At 1PM, the hour hand is 30º "ahead" of the minute hand, so I calculated the time to "catch up" as:

(5.5)T = 30    ....T = 5.4545454545454545 minutes after 1PM = 1:05:27 PM

And I realized that the same  1hr 5min 27 second interval would exist  ....so the remaining times are 

2:10:54 , 3:16:21, 4:21:48  and 5:27:15   [PM, of course ]

My last two times are off slightly because of rounding.....but...close enough  !!!

Mine isn't as "elegant"....but, maybe one day, I'll be as good as you guys....!!!

"I'll get you my two fine gentleman, and your little dogs, too  !!! "

It would be an honour!!!

:D

I need to improve ASAP!

No, MG1..I wasn't made a "mod" the day after I joined....I think it took about two days.....or, so.....

If you keep improving on your LaTex.....we might might make you "LaTex Assistant Supeviisor"  ....working under heureka and Melody, of course....!!!!!

you know what to do, mate.

promote Titanium Rome to:

Power user (required)

OR

Moderator

in exchange, the chimp will also become moderator and Titanium Romes' troops (us) will leave the Forums for good

Sorry, I had forgive the song... ( Just chorus )

I just wanna say thank you so much...

I dont know what did this web without you...

Before you leave, you can say us what this song says ( just chorus... )

ONCE AGAIN, SORRY FOR BAD ENGLISH...

i am glad now for you Titanium Rome. you, for the first time, have finally seeked peace in the forums

Very nice, guys......points galore to each of you...!!!

Make you moderator? The chimp has a better chance than you -- by ten-thousand times.

I would agree with CPhill and MathsGod1 as well

Thx, Melody

:)

P.S. if it was march 14, then CPhill would've became moderator on Pi Day. That's 2 holidays on March 14th.

Also, the Empire of Royality is holding a ceremony tomorrrow in memory of Mother's Day, 13th in memory of the empire, and the 15th in memory of my bday.

hello, this is Titanium Rome.

We have given you your friends back, and yes the locations are really far away.

The last step is to make me power user or moderator.

and then we're done fighting

That's insignificant, Alan! You and I spent a lot of time solving this problem not knowing that there's a shortcut...

here's that shortcut:

12 hours / 11 =1.0909090909090909 = 1h, 5min & 27.272727sec

or

720min / 11 =65.4545454545454545 = 1h, 5min & ~27sec

or

360^o / 11 =32.727272727272727^o  (converted into time units) = 1h, 5min, 27sec

Basically,  1h/5min/27sec  is an interval ( as your yesterday's graph shows) that repeats 11 times.

Once again, you did a good job! 

0! equals 1;

One of the ways to show this is to "complete the pattern":

$$\\5!=1\times 2\times 3\times 4\times 5=120
\\4!=\frac{5!}{5}=\frac{120}{5}=24
\\3!=\frac{4!}{4}=\frac{24}{4}=6
\\2!=\frac{3!}{3}=\frac{6}{3}=2
\\1!=\frac{2!}{2}=\frac{2}{2}=1
\\0!=\frac{1!}{1}=\frac{1}{1}=1$$

But that's where the pattern ends; you can't continue, because you end up with this:

$$(-1)!=\frac{0!}{0}=\textcolor[rgb]{1,0,0}{\frac{1}{0}}$$

See what I mean ?

#Mind-Blown!

$${\mathtt{0}}{!} = {\mathtt{1}}$$

I think anon can figure out what to do next after the method is given.

Some of my  answers are slightly inaccurate.  I rounded down all the "seconds" numbers, whereas I should have rounded them to the nearest second.  

Look at the time between 7 and 8 am for example.  Rounding your result to the nearest second gives 11 seconds, whereas I put 10 seconds.

I doubt if you could tell the difference when actually looking at the clock though!!

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Alright, Nauseated has finsihed his trial. he will be sent home by cruise and will return in 6 hours.

WE WON!!!!

WE ARE THE ULTIMATE CHAMPS!!!!

our reign continues to live, and we shall free the people, one by one. 

Katniss will be sent home as well in the same cruise

Rosala will be also sent home in 8 hours

And, I will return to the Titanium Headquarters in 48 hours after the cruises are done.

Exellent job, Alan! If you don't mind, I'll place my answer right beneath yours..

06:32:43.636363 AM

07:38:10.909090 AM

08:43:38.181818 AM

09:49:05.454545 AM

10:54:32.727272 AM

12:00:00         NOON

01:05:27.272727 PM

02:10:54.545454 PM

03:16:21.818181 PM

04:21:49.090909 PM

05:27:16.363636 PM

Multiply the number of degrees by pi/180.

If you are using the calculator and want the answer to a calculation in radians just put it into radian mode first (the Rad marker at the bottom left of the calculator).

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Here's a graphical solution (assuming I've understood the problem correctly!):

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