CPhill

5 + 12 - 5*√9 + 10 *√100 - 45 *2   simplify the radicals, first

5 + 12 - 5*3 + 10*10 - 45*2            perform the multiplications from left to right

5 + 12 - 15 + 100 - 90                     now.....just add and subtract

17 - 15 + 100 - 90 =

2 + 10 =

12

Call the distance from A to B, x  =AB

And A to C is 2x  = AC

Then, B to C = AC - AB

And AC - AB = 2x - x = x = 5, therefore, x = 5

Then, AB = x =  5 and AC = 2(5) =  10 ......

20 ft/ 13 sec = x ft / 3600 sec       cross-multiply

(3600 * 20)/ 13 =  about 5538.46 ft per hr   (a little more than 1 mile per hr)

It's possible if the worker is paid "double time" after 8 hrs.

So

$10 for 8 hours + $20 for 2 hrs. =

$80 + $40  =

$120

We have the position at any time is given by

P = -9.8t^2 + v₀t + h      where v₀ = 0.... and let P = 0 when it hits the water.....so we have

0 =-9.8t^2 + h    and at 1.2 sec, we have

9.8(m/s^2)(1.2 s)^2  = h  = about 14.1 m

The answer with no clasp is  = 5040.....the reason why is the we have a circle where the position of one of the shells is "set"......so we can arrange the others in 7! ways

With a clasp the answer is 40320, since when the clasp is undone and the braclet is laid out in a linear fashion, we have 8 ways to  choose which shell goes first in the chain, 7 ways to choose the second, etc.

Why does Pe^(rt) work??

Look at 

lim n →∞   (1 + r/n)^n

Let  m = n/r    So we have

lim m →∞ ( 1 + 1/m)^(r*m)  = 

lim m →∞ [(1 + 1/m)^m ] ^r       but ...    lim m →∞ (1 + 1/m)^m   = e

So we have

e^r

And

Pe^[r(1)]  = P(e^r) = would represent continuous compounding for one year

So....

Pe^(rt)  =

P(e^r)(e^r)(e^r)...........   where (e^r) is multiplied "t" times ....{representing "t" years (or periods)......}

And that's it.......!!!

At last, Nauseated

The die is cast

As Sisyphus hath said

And found

Such problems do not lend themselves

To Numbers

"Round"

Since all sides are the same, the side length is just 1 cm.

And the area is just the side length squared = (1 cm)^2 = 1 cm^2   ....!!!!

Since velocity is a vector quantity the average velocity is just (-15 + 10) / 28  = (-5/28)m/s

Average speed is a scalar......it's just total distance/time = (15 + 10) /28m/s  = (25/28)m/s

I believe this is correct......