CPhill

The length of the  diagonal  on the base of the  pyramid = 8sqrt (2) * sqrt (2)   =16

Hafl of this length  = 8

Height of the  pyramild =  sqrt  (10^2 - 8^2 ) = sqrt 36  = 6

Then the height of the  smaller pyramid =  6 - 4   = 2

These pyramids  are  similar  so the scale factor  is  2/6 =  1/3

Volume of the larger pyramid  =   (1/3) side^2  * height  =  (1/3) (8sqrt (2) )^2 * 6 = 2 * 128=  256 units^3

Volume of smaller pyramid =  volume of large pyramid * scale factor ^3  =  256 (1/3)^3 = 256/8 = 32 units^3

Thanks, Melody  !!!!

Good job, Spring   !!!

No prob  !!!

To make things easy, let  the box  length = 6  and the   box width =10  and the box  height  = 5

We can put 3 cubes along the length  and 5 cubes along the width.....thus....each layer of cubes contains 3 x 5 =  15 cubes

And we  can  stack  2  layers of cubes  =  2x15 = 30 cubes in total

The volume  of  the box is  6 * 5 * 10 =  300 in^3

The volume of the  cubes =  2^3 * 30  = 240 in^2

% of box volume taken up  by the  cubes  =  240 / 300  =  8/10  = 80%

5(x + 10)  =250     divide  both sides  by 5

x + 10  = 50          subtract 10 from both sides

x =  40

x  = number he ate on Monday

x + 4 =  Wed

3(x + 4)   = Fri

x  +  (x + 4)  + 3(x + 4)   =  26

x +  x  + 4  + 3x + 12 =   26

5x  + 16  =  26  

5x  = 26 - 16

5x   =  10

x =    2         on  Mon

x + 4  =     6   on Wed

3(6)  = 18  on Fri

a(a + 2b)  = 104/3

a^2  + 2ab    = 104/3      add b^2  to both sides and factor the  left side

a^2  + 2ab  + b^2 =    104/3  + b^2

(a + b)^2  =  104/3 + 7/9

( a + b)^2  =  313/9

sqrt [  (a + b)^2  ]  =   l a + b l

sqrt  [ 313/9 ]  =  l a + b l  =  sqrt (313) / 3

(a)

 5

 Σ C(5,n)  * (2x^5)^(5-n) *  [ (-1/9)y^4 ] ^(n)

n = 0

(b)

C(5, 2)  * (2x^5)^3  *  [ (-1/9)y^4]^2   =    10 * 8x^15  * (1/81)*y^8   =   80 x^15  y^8  / 81

12^(1/4) part  is correct

Angles  should  be 90° apart   = pi/2

Calculation of  angle,   θ  =    arctan  (6sqrt (3) / 6)   =  arctan  ( sqrt (3)) = pi/3

1st  angle = (  θ/4)  =   (pi/3)/4  =  pi/12

2nd angle=  pi/12  + pi/2 =  7pi/12

3rd angle  =  7pi/12  + pi/2 =  13pi/12

4th angle =  13pi/12  +  pi/2  =  19pi/12