CPhill

OK, catmg   !!!

cot x            cot x                 cot^2 x

____  *     _______  =       _______

  1               cot x                cot x

So

cot ^2x         csc^2 x

_____  -     _______  =  

cot x            cot x

(cot^2 x  -csc^2 x)

_________________

         cot x

OK.....glad to help .....

cot x  - ( csc^2 x  /cot x)                get a common denominator

cot ^2x   -csc^2  x

______________                 ( 1 + cot^2 x  = csc^2x   ⇒   cot^2 x   - csc^2 x  =  -1  )

    cot x

-1 /  cot x  =   

-1  / ( 1 /tan x) 

-1 (tan x)   =

-tan x

Not totally  sure about this one since oblique cylinders  don't  come along very often on here.....but  I  believe  that   we only need  the  radius and  height....the  axis  doesn't  matter

Using  this....the  volume  is  pi  * r^2 * h =   pi * (1.5)^2 * 3  = 

6.75 pi  yds^3    ≈  21.2 yds^3

Triangle ADB  is similar to triangle  BDC

So

AD  / DB =  DB / DC

3  / DB  =  DB  /  12       cross-multiply

12 * 3  = DB * DB

36  = DB^2

DB  = 6

AB = sqrt (DB^2  + AD^2)  =   sqrt  ( 6^2  + 3^2)    =  sqrt  ( 45)  =  sqrt (9 ) * sqrt (5)  = 3sqrt (5)

If 1 in  = 1 ft

Then the  model must have been 196  in tall

V =  area of  base  *  height  /  3

area of  base =  product  of leg lengths of  the right triangle  /  2  =   10 * 12  /  2   = 60

So

V =   60  * 20  /  3   =   1200  /  3     =   400 cm^3

We  have  two triangles  each with a base of 7.7m  and a height of  7.0 m

Their total area = 7 * 7.7    = 53.9 m^2

And we have two rectangles with dimensions of 8 * 18

Their total area =  2 * 18 * 8   = 288 m^2

Finally  we  have a 7.7  by 18  rectangle  in the  center  =  7.7 * 18   = 138.6 m^2

Area =  [  53.9 + 288 + 138.6 ]  =   480.5 m^2

We  have  to follow  the  triangle inequality  that  says  that  the sum of  the lengths of any two sides of a triangle  is  greater  than  the remaining  side

B is  out   because   1 + 2   isn't greater  than 3

C is out  because  2 + 2  <  5

D is out because   2 + 6  <  9

A is correct

6 + 8 >  9

6 + 9 >  8

8 + 9 >  6