CPhill

The radius of the larger circle is  20 cm

So  it's area  is   pi (20)^2  =  400pi cm^2      (1)

The area of both of the smaller circles is

2 * pi (10)^2  =  200 pi cm^2    (2)

So  the shaded area  is  (1)  - (2)  =

[ 400 - 200 ] pi  cm^2    =

200 pi   cm^2  =

200 * (3.14) cm^2 =

628 cm^2

C = 28pi    ft

C  =  2pi *r        so

28pi  =  2pi *r       divide both sides by 2pi

14 feet  = r

28 feet  = d

Area  =  pi * (r)^2   =  pi * (14)^2   =   196pi  ft^2

Let H be the tree height....so we have

H / 35  =  9 / 7      multiply both sides by 35

H  =  (35 * 9)  / 7   =  (35/7) * 9  =  5 * 9  =  45 ft

The diagonal will be the hypotenuse of a right triangle...so..its length is

√  [ 22^2  + 6^2  ] =

√ [ 484 + 36 ] =

√ 520  ≈  

22.8 ft

.8  of 1 foot  =   .8 * 12  inches  =  9.6 in

So...the length is ≈    22ft  9.6 in

2n ,  n^2   - 1, n^2  + 1

2*7  , 7^2 - 1 ,  7^2  + 1

14 , 48,  50

Edit to correct an error.....!!!

7  ,     (7^2 - 1) /  2   ,  (7^2  + 1) / 2  =

7   ,         48/2         ,          50/2         =  

7    ,         24          ,           25   

Not sure about the first one, J....but the second is this :

The angle in rads is given by :

arctan (2/4)  + pi/2  =

arctan (1/2) + pi/2  =  

2.034 rads

So....you are correct.......!!!!

We have the following proportion :

19 / 50   =  h / 325   where h is the building height

Multiply both sides by 325  and we have

h  =  [ 325 * 19 ] / 50  = 123.5 ft

Draw BD....   and this forms a hypotenuse of  triangles ABD  and triangles BDC

In triangle   ABD , we can find BD using the Pythagorean Theorem

BD  =  √[ AD^2 + AB^2 ]  = √ [ 12^2 + 5^2 ]  = √ [ 144 + 25]  = √169  = 13

And  using the same theorem, in triangle BDC, leg DC can be found as

DC  =  √ [ BD^2  - BC^2]  = √ [ 13^2 - 11^2]  = √ [169 - 121]  = √48 = √[16 * 3]  =

√16 * √3  =  4√3

And the area of each right triangle = (1/2)(product of the legs)

So....the total area  =  (1/2)(12 * 5) + (1/2) (11 * 4√3)  =

(1/2) [ (12*5) +  (11 * 4√3) ]  =

(1/2)  [ 60 + 44√3]  =

[30 + 22√3]  sq units 

There are 4 periods in each second

So....eaach period lasts 1/4 seconds

At t = 0,  let the height = 1 m 

So...at  1/16 seconds  the max ht is reached

At 2/16 seconds the height returns to 1m

At 3/16 seconds, the min height is reached  = 1m - .03m  = .97m

And at 4/16 = 1/4 second it returns to a height of 1m 

Note that the sin is maxed at pi/2

So....at  1/16 seconds....we have that  .03 sin (8pi *1 /16) + 1  =  .03sin (8pi/16) + 1  =

.03sin (pi/2) + 1 =  .03(1) + 1  =   .03 + 1  =  1.03m

So.....the function  is

h(t)   =  sin ( 8pi * t)  +  1    =   choice " a "

See the graph here :  

https://www.desmos.com/calculator/f9yuhgchgr