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wait i checked with calculator and this is wrong so i dont know where i slipped up

10/3sqrt5

(10/3)/((3sqrt5)/3)=

3.33/sqrt5

3.33²/sqrt5²=

11.11/5

11.11/5=20/9 so

10/3sqrt5=20/9

GCF(2016093008, 8003906012)

factor(2016093008) = (2^4*97)*1299029            = 4*4*97*1299029

factor(8003906012) = ((2^2*821)*1511)*1613    = 4*821*1511*1613

GCF = 4

-8.8x=-64

--> 8.8x=64

--> x=64/8.8

--> x=7.2727272727...

Yep

solve

\(9sin[\frac{2\pi}{24}(x-8)]+45=41\)

Y = 1 / (1 - X)

THAT WAS HILARIOUS!!

Thanks for sharing Ginger :))

Curly is soitenly my favorite. 

Here's a clip of the funniest of all.

It makes perfect sense..however...I still have to wrap my  mind around the  2pi/24  part....!!!!

Well, I would like to be sitting right behind them! nyuk nyuk nyuk

I love the three stooges!

I stole this one from Melody..........you can see the methodology  in  her answer to your other post

Here's the graph :

It is first 41° at  t ≈ 6.25 hrs  after midnight ≈ 6:15 AM

Thanks Chris,

I am sure it can be done much easier, the time is not a difficult one, but I just decided to do it like this.

I suppose if I was good at it, and did not have to think at all, it would be a dead simple method but at present I still have to think about what is happening.  

Cuboid volume = V = l x b x h

re-arranging

V/(l x b)  = h  

You've some pretty big numbers there.......

"...consistently 1,000,000,000,000,000 calculations for second..."    needs clarification.....is that the DAILY AVERAGE PER SECOND ...or the height of brain activity in any given day?    If it is the former, then just divide your yearly calculation by 365 to get the daily average !   G'Luck !!   Think On !   LOL

Nice, Melody....!!!!

$30 / 1hr  x  1.5 hr = $ 45

So  T^2 is PROPRTIONAL to P^3

T^2/R^3 = 4 pi^2 / G M   

    where G = graviational constant    6.67408 x 10^-11 m^3/kg-s^2     M= sun Mass = 1.989 x 10^30kg

(88 days x 24 hours x 3600 sec/hr)^2 / P^3 =  2.973949 x 10^-19

P = 5.7927 x 10^10 m

= 57,927,719 km  from Sun

typo error :

"The centre of the wave is y=65 so the wave is 'lifted' by 64"    that should have been lifted by 65.

how many times does 6 go into 84?

A sign wave is of the form  (I am developing the graph in radians)

y=sinx

This has a amplitude of 1 a centre y=0  and a wavelength of  2pi  

\(y=sin(x)   \qquad \text{ has a wavelength of }2\pi\\\ y=sin(nx) \qquad \text{   has a wave length of }  2\pi\div n\ so\\ y=sin(\frac{2\pi }{24} *x) \qquad \text{ has a wave length of }2\pi\div \frac{2\pi }{24}=24 \text{ and this will represent hours.}\\\)

So so far we have

\(y=sin[\frac{2\pi}{24}(x)]\)

Now the amplitude of the wave is 15 degrees (80-65=15)

\(y=15sin[\frac{2\pi}{24}(x)]\)

The centre of the wave is y=65 so the wave is 'lifted' by 64

\(y=15sin[\frac{2\pi}{24}(x)]+65\)

The hottest part of the day is 5pm=17:00 in 24 hour time, so the average temps must be 6 hours either side,  11:00 and 23:00

So at 11:00 the is average temp but getting hotter.  So the horizonal shift is 11 in a positive direction

\(y=15sin[\frac{2\pi}{24}(x-11)]+65\)

So at 3am it will be  

15*sin(2pi/24(3-11))+65 = 52 degrees

Here is the graph:

Full interactive version:

C^1.85 = 89390724.39     raise each side to  (1/1.85)

[C^1.85]^(1/1.85)  = 89390724.39^(1/1.85)

C  = 89390724.39^(1/1.85)  ≈  19860.76

....and I agree with Chris'  second answer    !!!   

I agree with EP's first answer........

I see the second situation a little differently

We can arrange Larry, Curly and Moe  in 3!  ways in the front row and the other students in 6! ways in the other desks....so

3! * 6!  =  4320 arrangements

92/80  =

1.15  goals per game