CPhill

3.2 + e^(6x) = 54.2      subtract 3.2 from both sides

e^(6x)  = 51     take the LN  of both sides

LN e^(6x)  = LN  51     and we can write

6x LN (e)   = LN 51       and LN = 1 so we can ignore this....and we have...

6x  = LN 51      divide both sides by 6

x = LN (51)  / 6    = about   0.6553

tan^-1(0.5)  = about  26.565° 

What is the magnitude of an earthquake, y, that is 10 times as intense as the previous earthquake (rounded to the nearest tenth)?

y = log 10 + 7.9 =  1 + 7.9 =   8.9

What intensity, x, is the aftershock with a magnitude of y = 8.7 (rounded to the nearest whole number) compared with the original 7.9 earthquake?

8.7  = log x + 7.9     subtract 7.9 from both sides

0.8  = log x

This  says that x =   10^0.8  = about 6.3  = about 6  [rounded to the nearest whole number]

We did....and Goodnight, DS   !!!!

3 + 10   / 2  =

3 +  [ 5 ]  = 

8  !!!!

Rarinstraw....here's a whole page devoted to the Fibonacci Series....it's pretty interesting...:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html#relprime

And here's one dealing with Binet's Formula :

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html#Binetneg

Here's my best shot at this one....

Assuming 30 days in a month, there are 30 days//2.5 days = 12 producing cycles in the month

And in each of these cycles......1/2 of an egg is produced....so.....12 * 1/2  =  6 eggs are produced in a month by 1 1/2 chickens

Then......1 chicken  must be able to produce only  2/3 of what 1.5 chickens can produce in a month  since 1/1.5  = 2/3.....so......(2/3) * 6   = 4 eggs

F(20) = [ Phi^20 - (-phi)^20 ]  / √5   =  [ Phi^20 - (phi)^20 ] / √5  =

( [ (1 + √5) / 2]^20  - [2 / (1 + √5)]^20 )  / √5 =

6765

[ It's quite surprising that dividing by an irrational produces an integer result....!!! ]

Pi = the ratio of a circle's circumference to its diameter.....