CPhill

A "monomial" is just a single term like 3, 5x, (1/2)x, etc.

"Mono"  means "one"

Notice

1 + 2 = 3

2 + 3 = 5

3 + 4 = 7

4 + 5 = 9

So.....for any nth pair, the sum is just 2n + 1

Here's one of them.......

Here's (14)

.002 = e^(-.00012* t)      take the ln of both sides

ln .002 = ln e^(-.0002 * t)    and we can write

ln.002  = (-.00012 * t) ln e      and ln e = 1, so we can ignore this......so we have

ln .002  = -.00012 * t       divide both sides by -.00012

t = ln .002 / -.00012  = about 51,788 years old

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{96}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{10}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{96.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
{\mathtt{x}} = {\mathtt{0.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
\end{array} \right\}$$ 

Here's  (15)

199200  = 80000(1 + r)⁵     divide both sides by 80000

2.49  = (1 + r)⁵       take the log of both sides

log 2.49  = log (1 + r)⁵    and we can write

log 2.49 = 5 log ( 1 + r)    divide both sides by 5

log2.49/5 =  log (1 + r)     

.079 = log(1 + r)   and in exponential form ,we have

10^.079 = 1 + r

r = 10^.079 - 1   = .20  = about 20% per year

972 pi  = (4/3) * pi * (r^3)     divide both sides by pi

972  = (4/3) * r^3      multiply both sides by 3/4

729 = r^3      take the cube root of both sides

9 = r    and the diameter is twice this  = 18

e^-x = 9/2    this is equivalent to :

e^x = 2/9       take the ln of both sides

ln e^x = ln (2/ 9)    and we can write

x ( ln e ) = ln (2/ 9)       and  ln e = 1   ....  so  .....

x = ln (2/9)  ≈ -1.504

6N + 8 = 32      subtract 8 from both sides

6N = 24             divide both sides by 6

N = 4      and that's the number.....!!!!

Let's see.......

2 quarters  1 nickel

1 quarter  3 dimes

1 quarter 2 dimes  2 nickels

1 quarter  1 dime 4 nickels

1 quarter 6 nickels

5 dimes 1 nickel

4 dimes 3 nickels

3 dimes 5 nickels

2 dimes 7 nickels

1 dime 9 nickels

11 nickels

I think that's it......did I leave anything  out ???