CPhill

2 ( 12 + x )  =  33 + x         where x is the number of years

24 + 2x  = 33 + x      subtract x, 24 from both sides

x  = 9

7 times intense

y = log(7) + 7.9 = about 8.7

Intensity comparison

8.9 = log x  + 7.9      subtract 7.9 from both sides

1  = log x        and x = 10

So  (D)  is correct

We can use the sine function to model this

sin(50) = H / 50       where H is the height    ...   multiply both sides by 50

50*sin(50) = H  = about 38.3 ft

-69= 7V - 6   add 6 to both sides

-63  = 7V      divide both sides by 7

-9   = V

This doesn't have a fractional equivalent.....the value is ..   -0.900968867902......

1,000,000 = 10,000e^(.1t)   divide both sides by 10,000

100  = e^(.1t)    take the natural log of both sides

ln (100)  = ln (e)^(.1t)    and we can write

ln (100)  = (.1t) ln e     and ln e = 1   so we can ignore this

ln(100)  = .1t        divide both sides by .1

t = about 46.05 years

Kate   150  Jess

200             170

                   Kiki

We can find the angle thusly :

arccos [170^2 - 150^2 - 200^2] / [ -2(150)(200)]  =  about 55.9°

343m *  1km / 1000m  =   0.343km / s

Let A  be the first place prize......then we have

A + [ A - 50] + [A - 100 ]  +  [A - 150] + [A - 200] = 1000  simplify

5A - 500  = 1000    add 500 to both sides

5A  = 1500      divide both sides by 5

A = $300

A - 50   = $250   for second place  .....   and so on........

n^3/3+n^2/2+n/6  =   [2n^3 + 3n^2 + n]/ 6

n^4/4+n^3/2+n^2/4  =  [ n^4 + 2n^3 + n^2] / 4

So.....the sum of these  =

[ 4n^3 + 6n^2 + 2n + 3n^4 + 6n^3 + 3n^2 ]  / 12    =

[ 3n^4 + 10n^3 + 9n^2 +  2n ] / 12

Here are the sums :

1 | 2

2 | 14

3 | 50

4 | 130

5 | 280

6 | 532

7 | 924

8 | 1500

9 | 2310

10 | 3410