CPhill

Neat, Melody....that was a lot of work.....!!!!

arcos (0.10)  ≈ 84.3°

Note to above......if we're not summing the accumulated amounts but  just doubling the amount each day.......for any day "n".....the amount for that day [ in cents ]  is 2^n-1

Assuming a 30 day month...we have

Sum  = 

Beginning amount in cents * [  1 - (ratio beween terms)^no. of days ] / [1 - ratio beween terms ]   =

1 * [ 1 - 2^30 ] / [1 - 2]  = 1073741823 cents  = $1,073,741,823

This simplifies to :     2ⁿ - 1  = 2³⁰ - 1  = 1073741823 cents  = $1,073,741,823

The second is obviously easier to deal with....!!!

Also....." n" can be any number of "doubling" days......

This big......

1^6 - 2^6 + 3^6   =  666     ....OR......

The sum of the 1st 36 positive integers ......OR....

4+9+25+49+121+169+289  =

2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2  =  666 =  sum of the squares of the 1st seven primes...!!!

We try to answer as many questions as possible......no guarantees, though....

Isabelle is correct...we use this.....

Ext angle°   =  360 / n     where n is the number of sides

So

72 = 360 / n        rearrange  as

n  =  360 / 72   = 5 sides  [ a pentagon  ]

Correct-a-mundo.....!!!!!

V = (1/3) * 3.14 * R^2 *H       ..... R = 2 3/4→ 2.75   and   H = 4....  so we have...

V = (1/3) * 3.14 * ( 2.75)^2 * (4)  ≈  31.66 units^2

Very nice, Isabelle......!!!

BTW.....the second answer can be derived as follows :

( # sides in a heptagon - 2) (180)°  / ( # sides in a heptagon)  =

( 7 - 2) (180)° / 7  =

(5/7) (180) ° ≈   128.6 °