CPhill

I think Melody just "drove" home that point .......!!!

Here's my take on this.......

T ^ F ^ T  =

(T ^ F)  ^ T =

(F) ^ T  =

F

To verify this....here's is the truth table for a^b^c = p^q^r....the third row shows the result for  T^F^T

(1/4 x ) = (4x7) -6

(1/4)x = (28) - 6

(1/4)x = 22   multiply by 4 on both sides

x = 88

(0! + 0! + 0! +0! + 0!)! =

(1 + 1 + 1 + 1 + 1)! =

5! =

120

I'm assuming that the "directly overhead" refers to "directly ovehead" the weather office.

We need the tangent function, here. Note that, we know the amgle of elevation, and the distance that the searchlight is from the weather office. And we're looking for the opposite side of the angle (the height of the clouds above the ground).....so we have

tan(35) = h/200    where h is the height of the clouds...

I can provide a general diagram....if you need it......

The first thing that we can do is to find the slope....this is given by the change in y divided by the change is x.

y changes from -4 to 2   =  6       And x changes from -10 to -1  = 9

So the slope is 6/9   = 2/3    So, every time y changes by 2,  x changes by 3.  Put another way, everytime x changes by 1, y changes by 2/3.

And the y intercept is where x = 0.  So from -1 to 0, x changes by 1 and y changes by 2/3. So 2 + 2/3 = 8/3.

So the y intercept  is   (0, 8/3)

Well....here we have an angle, the adjacent side, and we're looking for the hypoteneuse (the rope length).

The thing that relates all of these is the cosine.   So we have......

cos(13) = 25/h      where h is the rope length.    Rearranging, we have

h = 25/cos(13) = about 25.66 ft.   (rounded to the nearest hundredth ft)

I should have said "make up" rather than "catch up." What I meant was that, if you accidentally (or maybe, even on purpose) fail to keep your promise of fasting one one or more days.......can you "atone" or make up for this at a later time???  I've heard that this is allowed in some places.......but frowned upon in others !!!

Wow!!!....that was fascinating, rosala........you're correct..........Ramadan in 2021 begins in the early part of April !!

Are you allowed to "catch up" for missed days at a later time?? I've heard that this is allowed in some places...

P. S.  .......those dates in that market place look yummy.........they are really expensive here in the US......I like them, but I can rarely afford them !!!

Thanks, Alan...this is derived from "Binet's Formula" which allows the calculation of any Fibonacci number, (n).

The "formula" is given by:

F(n) = [(Phi)ⁿ - (-phi)ⁿ] / √5

Where      Phi = [√5 + 1] / 2      and     phi  =  [√5 - 1] / 2       So we have........

F(n) = [ ((√5 + 1) / 2)ⁿ -  ((1- √5 ) / 2)ⁿ ] / √5 =  [ (1 + √5 )ⁿ -  (1- √5 )ⁿ ] / (2ⁿ√5)

This webpage has some fascinating facts and properties of the Fibonacci Series.......it's one of my favorite math sites on the internet!!!