CPhill

All we need to do is to look  at 8^(2/3)  = [ (8)^(1/3) ] ^2   =  [cube root of 8] ^2  =   [2] ^2 =  4

The last answer is the only one that works

sqrt (144)  = 12    (1 + 2)^2     = 9  = 1 + 4 + 4

sqrt (169) = 13     ( 1 + 3)^2  = 16  =  1 + 6 + 9

sqrt ( 196)  = 14    ( 1 + 4)^2 =  25  but 1 + 9 + 6  =   16

100°

To convert from degrees to radians use  ( pi / 180)

So

100  * (p /180)  =   (10/18) pi   =   (5/9) pi  (rads)

a^2  = k / b^3       where k  is the proportionality constant

3^2  = k / (7)^3

k =  3^2  / 7^3  =   9 / 343   

So

a^2  = (9/343) / 6^3  =  9 / [343 * 6^3 ] =  9 / 74088  =  1/ 8232

h(t)  =  t^2  - 12t  + 27

Factored form

h(t)  = (t - 9) (t - 3)

Look at the graph here (in x  rather than t)  :   https://www.desmos.com/calculator/gug8sulzit

We can interpret this graph as follows

At t =  0 sec, the diver is  27 feet above  the water

At t = 3 sec, the diver hits the water

At t = 6 sec, the diver is  9 ft below the surface

At = 9 sec, the diver returns to the surface

True statements

The swimmer comes back up 9 seconds after the timer was started.

The swimmer dives into the water 3 seconds after the timer was started.

(-5 + 2i) (1 + 7i)   =

-5*1  + (-5)(7i)  + (2i)(1) +  (2i)(7i)  =

-5  - 35i + 2i + 14i^2  =

-5  - 33i + 14 (-1)  =

-5 -33i - 14  =

-19 - 33i

Each dimension of the dilated cone will have a scale factor of  sqrt [  (2250 / 360)] =  sqrt (6.25)  = 2.5 

So...the dilated cone's volume =   800pi * (2.5)^3  =  12500 pi  (in^3)

We have the form

f(x)  =  Acos(Bx + C) + D

A = the amplitude  =   (10 -  -4) / 2 =  14 / 2  =  7

B=    (2pi)  / the period     =  (2pi) / ( pi/2 ) =  4

C =  the phase shift =  there is none

D =   the midline  =  (10  - 4) / 2  =  6/2  = 3

So....our function is

f(x)  = 7cos (4x) + 3

See here :  https://www.desmos.com/calculator/ffmw4ugln0

Y

X        Z

tan Y  =  XZ / XY =   3/2   ⇒   XZ =  (3/2)XY

Therefore, by Pythagoras

XY^2  + XZ^2  = 80^2

XY^2  +  [ (3/2) XY ] ^2  =  6400

XY^2  + (9/4)XY^2  = 6400

(13/4)XY^2  = 6400

XY^2 =  6400 / (13/4)

XY^2  = 6400 * 4  / 13

XY  =   sqrt [   (6400 * 4 )  / 13  ]  =   160  / sqrt 13  ≈  44.38

THX, Guest....I realized later that mine was wrong  !!!!