CPhill

Note that we have a right triangle..... and  since they are co-functions...sin P  =  cosR

And cos P  =  sin R

So

sin R  - cos R  =

cos P  - sin P   =

0.8192   -  0. 5736  =

0.2456

1.    Correct   !!!!

2.   Not sure about this...but... I believe that you are correct

3.   Correct !!

4. The radius of circle V is 16.  Correct!!

Also...Circles V  and W  are similar because all circles are similar...

5. Correct  !!!

Call the height, h

Since the apex angle  is a right angle... the height is forms a geometric mean, thusly 

16/h  = h/4      cross-multiply

h^2  =  64

h  =  8

And by the Pythagoren Theorem

√ [ h^2  + 4^2  ]  =  y

√ [ 8^2 + 4^2 ] = y

√80  =  y

√[16 * 5]   y

4√5  = y

y / 10   =  [  y + 4  ]   / 15   cross-multiply

15y  = 10y + 40

5y  =  40

y  = 8  

( ⁿ√a) ^m   can be written as    a^m/n  .....so.....

⁵(√a⁵ )  =    a^5/5  =  (a^1/5)⁵  = a  ⇒   Answer  C

Second one

³√ [216a³b9 ]  =  ³√216  * ³√a³  *  ³√b⁹    =  (6³)^1/3 * (a³)^1/3 * (b⁹)^1/3  = 

6ab³ ⇒ Answer C

Last one....look at answer B

√[98 j⁹c⁸]  = √{49*2]  * √ [j⁹ ] * √[c⁸ ]   =

√49  * √2  * √ [j⁸]  * √j  * √[c⁸ ]   =

7  * √2  *  (j⁸)^1/2  * √j  *  (c⁸)^1/2    =

7j⁴c⁴√[ 2j ]   

log ( x + 2)  = 1 + log (x)

We can write

log ( x + 2)  -  log (x)  =  1       using a log property, we have that

log [ (x + 2) / x ]   = 1       in exponential form, we have

10 ^1   =  [x + 2] / x

10  =  [ x + 2] / x      multiply both sides by x

10x  = x + 2   subtract x from  both sides

9x  =  2    divide both sides by 9

x  = 2/9  ≈ 0.222

30  out of 40 dislike the new start time  = 3/4

So....we would expect that   (3/4)*1000  =  750  to dislike it

Call a side,  S

The perimeter  is 6S

The area  = 6* (1/2)S^2 (√3) /2   = 6*(√3/4) *S^2  = (3√3/2)S^2 

So  

P^2  / A  =    (6S)^2  / [ (√3/3/2) *S^2 ]   =  

  36                        72               24

______   =            ___    =       ___    =  8√3

(3√3) /2                3√3              √3

We can use a weighted average here  =

[ sum of  freq* mipoint ] / [sum of freq ]  \

[  (1*5) + (4*15)  + (7 * 25)  + (2 * 35)  + (3 * 45)  + (3 * 55)

_______________________________________________

     [ 1 + 4 + 7 + 2 + 3 + 3 ]

[  610 ]

______

   20

30.5  cm  =  mean height of the plant

Area  of a trapezoid  =

height  * ( sum of base lengths)  / 2

So...let the height  = h

One  base  = h + 3

And the other is h + 5

So...we have this

375  =  h [  (h + 3  + h + 5 ]  / 2      multiply both sides by 2

750  =  h [ 2h + 8 ]

750  = 2h^2 + 8h      rearrange as

2h^2 + 8h   -  750   =  0 

Using the quadratic formula....we get the answer  ≈  17.468  =  17.5 yards (rounded)   

"b" is correct