CPhill

I think you might want to find this:

sinx  = (200/900)  = (2/9)       using the sine inverse, we have

arcsin (2/9) = about 12.84°

If you end up with a negative under the radical, it means that there is no real solution [ you will have two "complex" solutions involving  "i"  ]

56.6 - 3.2   = 53.4 ml

(1/2) 53.4 = 26.7 ml

26.7 - 6  = 20.7 ml    remained in the bottle

-(1/8) + (3/4)  =

-(1/8) + (6/8)  =

5/8

So

∛(5/8)  = 

∛5 / ∛8   = 

[∛5 ] / 2

3 + 3/8 =   27/8

And 3/4  = 6/8

So...the first  four numbers are :

27/8, 21/8, 15/8, 9/8

BTW  .....The nth term is given by : [  27/8  - (3/4)(n - 1)  ]  =  [  33/8 - (3/4)n ]

2 + 1/2  =  5/2   ......so....

[800]  / [ 5/2]  =

[800 / 1 ]  / [5/ 2]       invert the second fraction and multiply

800/1   *  2/5   =

1600 / 5  =

320

x+2y=7     rearrange this as  x = 7 - 2y   (1)

2x+2y=13    (2)

Substitute (1)  into (2)  for x   and we have

2[ 7 - 2y] + 2y = 13

14 - 4y + 2y  = 13

14 - 2y  = 13       subtract 14 from both sides

-2y  = -1              divide both sides by -2

y = 1/2

And using (1) ....  x = 7 - 2(1/2)  =  7 - 1   = 6

So     ...      {x, y}   = { 6, 1/2 }

24 :  3  =

8 : 1

8/8 + 5/8 + 7/8 + 8/8 + 8/8 + 5/8 divided by 6

[1 + 5/8 + 7/8 + 1  +  1 ]  / 6  =

[ 3 + 12/8] / 6  =

[3 + 1 + 4/8]  /  6  =

[4 + 1/2] / 6  =

[ 9/2] / [ 6/1]  =

[9/2] * [ 1/6] =

9/12  =

3/4  =

0.75 =

75%

3x= 4y+10     multiply this equation through by 4 =   12x =  16y + 40   (1)

4x= -3y+11    multiply this equation through by -3  = -12x =   9y  - 33   (2)

Add equations (1)  and (2)

0 = 25y + 7   subtract 7 from both sides

-7  = 25 y     divide both sides by 25

-7/25  = y

And substituting this value for y into (1) to find x, we have

3x = 4(-7/25) + 10

3x = -28/25 + 250/25

3x = 222/25  divide both sides by 3

x = 222/75   = 74/25

So {x, y}   = { 74/25 ,  -7 / 25 }