CPhill

3.   We have 8 congruent 30-60-90 triangles

The base of each  =  4.6/ 2   =  2.3

The height of each is opposite the 60° angle  = √3 * base  = √3 * 2.3

So.....the lateral surface area  is

8 (1/2) (base) (height) =

4 (2.3)(√3 * 2.3)  ≈  36.65 yd^2 

The base area  =  side^2  =  4.6^2  = 21.16 yd^2

So....the total area  is     36.65 + 21.16  =  57.8 yd^2

We have a 30-60-90 triangle

The side opposite the 30°  angle  =  1/2  of the hypotenuse  = 6

The side opposite the 60°  angle  is √3  times this  =  6√3  =  x

Area  =   1/2 (diameter/2)^2* (theta in rads)  =

1/2 ( 21.2 / 2)^2 (3 *3.14 / 5 )  =

1/2 ( 10.6)^2  * (3 *3.14 / 5)  ≈   105.84 cm^2

1. The first term is 5......you should be able to take it from there, NSS

2.   a₁  = 14 ,  a_n  = a_n-1 - 4

3.  -13 + 7(n - 1)

14

First term  =  6(1) - 4  =  2

16th term  =  6(16) - 4  =  92

Sum  = 

(first term + last term) (number of terms) / 2  =

 (2 + 92) * 16/2  =   94 * 8   = 752   

15.  Similar to 14

First term  = 4(1) - 3  = 1

!0th term  = 4(10) - 3  =  37

Sum  =

(1 + 37) * 10/ 2  =

38 * 5  =

190

2.  For the lateral surface area, we have 8 congruent triangles  each with the same base as the height because both are opposite 45 degree angles

The base of each triangle  =  height  =  5

So....the lateral surface area  =

8 (1/2) (base) (height)  =

4 (5)(5)  =  100

The area of the base  is just  side^2  =  10^2   =  100

So.....the  surface area  =  100 + 100  =   200 ft^2

1.  We have 12 congruent triangles here

We can find the base of each  as

cos 60  =  base/14    

 1/2  = base / 14      multiply both sides by 14

7  = base

We can find the height of each as

sin 60  =  a / 14     

√3/2  = a / 14    multiply both sides by 14

7√3  = a

So......the area of the hexagon is

12  * (1/2) (base)(height)  =

6 ( 7) (7√3)  =  294√3  cm^2

Diverges.....the common ratio between terms   ≥ 1

Thus....it deoes not have a definite sum

Here's the first two

1.  Avg Rate of Change

f(9)  - f(5)            14 - (-2)             16

_______    =     _______   =        __       =      4

  9  -  5                 9 -   5                4

2.   (f/g)x   =  [ 4x^2 + 6x]  /  [ 2x^2 + 13x + 15 ]  =  [ 2x (2x + 3)] / [ (2x + 3) (x + 5)]  =

2x / (x + 5)

Avg Rate of change  =

f(0)  - f(-3)                1/2   -  2              -1.5            -1

_________   =        _______     =       ___     =    ___

   0  -  (-3)                     3                       3               2