CPhill

We can use the arctangent here

arctan (3/4)  = C ≈  36.87°

Second one..we know the opposite side to R and the hypotenuse...so....we can use the arcsin

arcsin (30/40)  = R ≈ 48.59°

(n - 3) / (n^2 + 6n + 8)

_________________

        (n + 1)

        _____

        (n + 2)

    ( n - 3)                          ( n + 2 )

___________    *            ________

n^2 + 6n + 8                     ( n + 1)

(n - 3) (n + 2)

__________________

(n + 4) ( n + 2) (n + 1)

(n - 3 ) ( n + 2)

____________

(n + 4) ( n + 1)

d^2 - 9d + 20           d^2  -2d - 8 

___________  +    ______________

d^2  - 3d - 10          d^2  +4d  - 32

(d -5) ( d - 4)    +    (d -4) (d + 2)

___________         ___________

(d - 5) ( d + 2)        (d + 8) ( d - 4)

(d - 4)       +    (d + 2)

_____            _____

(d + 2)            (d + 8)

(d - 4)(d + 8)  +  (d + 2) (d + 2)

________________________

      (d + 2)  (d + 8)

d^2 - 4d + 8d - 32  + d^2 + 2d + 2d + 4

_______________________________

   (d + 2) (d + 8)

2d^2  + 8d - 28

_____________

(d + 2) (d + 8)

Very nice, Omi   !!!!

Horizontal  asymptote  =  y  = -4/8  =   -1/2

See my answer here :

https://web2.0calc.com/questions/need-some-help_11

We have the following relationship :

MN  ( MN + NO)   = MP ( MP +  PQ)    which means that

MN ( MN + NO)  =   MP(MQ)

NO  =  6

MN  = 3

MQ  = 15

So 

3 (3 + 6)  = MP (15)  

3 (18)  =  15 * MP   

54  =  15 * MP      divide both sides by  15

54/15  = MP   =  18/5

2.  In  an inverse relationship......the number of people  * cost per person = total cost is constant

So....the total cost  is

44 * 30   =  $1320

So.....to find the cost per person if 20 pepole go we have that

20 *  cost per person  =  1320        divide both sides by 20

cost per person  =  1320 / 20   =  $66

Area of sector  =  (1/2)r^2 * (theta in rads )

So

15.3  = (1/2) (3)^2 *  ( theta in rads)

15.3   =  9/2   * (theta in rads )       multiply both sides  by  2/9

15.3 (2/9)  =  (theta in rads)

3.4   =   theta  in rads

To  conert this to degrees  we have

3.4    *  180° / pi   ≈  194.8°

To  find the arc length, S,     we have

S    =  2 * pi  (radius)   (194.8 / 360)  =

2 * pi * 3  *  (194.8 / 360)  =  

6* ( 194. 8 / 360)  * pi   ≈   81.26 m

To convert the exponential form   b^x   = n      to log form   we have

log_b n  =  x

So

10^x  =  25    becomes

log₁₀ 25  =  x

So    b  =  10      x =  x        and    n  =  25   

Hope that's not too confusing !!!