CPhill

Here :  https://web2.0calc.com/questions/graphing-parabolas_8

sin A = 3/4  = BD / BA

3/4 = BD / 24

(3/4)(24) = BD = 18

sin C =  1/4  =  BD / BC

4BD = BC

4 (18) =  BC = 72

DC =  sqrt [ 72^2  - 18^2 ]  =  sqrt  [ 18^2 ( 4^2  - 1^2) ] =  18 sqrt (15)

.97777.... =

(97  - 9)  / ( 90) =  88/90  = 44/45

a -  b =   44  -  45  =   -1

By a little inspection.....let x = 16 and y=  81

sqrt (16) + sqrt (81)  =

4 +  9 =   13

And

4 (16) + 9(81)  = 793

So....x =  16

3

18 mod 3  = 0

16 mod 3  =  1

****

The hour hand moves  at (1/2)°  every minute  

The minute hand  moves 12 times as fast = 6° every minute

From  12 Noon....the  hour hand has moved  (1/2)° (48)  = 24°

The minute hand has moved  (6°) (48)  = 288°

The larger obtuse angle between them  =  (288 - 24)°  =  264°

The smaller obtuse angle between them = (360 - 264)°  = 96°

Lateral suface area  =  2 * pi * r * h

3.5 = 2*pi * r * h  →       solve for h

(3.5) / ( 2 * pi * r)   =  h

Volume =  pi * r^2  * h

5 =  pi * r^2 *  ( 3.5) / ( 2 *pi * r)

5 = 1.75 r

5 /1.75  =  r   =  20 / 7  in 

sqrt (27) * sqrt (12) * sqrt (300) =

sqrt (9) * sqrt (3)  * sqrt (4) * sqrt (3)  *  sqrt (3) * sqrt (100)  =

3 * sqrt (3) * 2 * sqrt (3) * sqrt (3) * 10  =

3 * 2 * 10 * [sqrt (3) * sqrt (3)] * sqrt (3) =

3 * 2 * 10 * 3 * sqrt (3)  =

180 sqrt (3)

sqrt (2) * sqrt (6) * sqrt (110) * sqrt (156)   =

sqrt (2)  * [ sqrt (2) * sqrt (3) ] * [ sqrt (11) * sqrt (5) * sqrt (2) ] * [sqrt (4) * sqrt (3) * sqrt (13) ] =

sqrt (2) * sqrt (2) * sqrt (2) * sqrt (4)  *  sqrt (3) * sqrt (3) * sqrt (11) * sqrt (13) * sqrt (5)  =

2 * sqrt (2) * 2 * 3 * sqrt (11) * sqrt (13) * sqrt (5)  =

12 *  sqrt  [ 2 * 11 * 13 * 5 ] =

12 sqrt [ 1430 ]