Aright rectangular prism has these dimensions:
length − fraction 1 and 1 over 3 units
width − fraction 5 over 6 unit
height − fraction 2 over 3 unit
how many cubes of side length 1 over 6 unit are required to completely pack the prism without any gap or overlap?

The number of cubes required is .

Step-by-step explanation:

The dimensions of the right rectangular prisms are

The volume of the right rectangular prism is

.

We substitute the dimensions to get,

.

We convert the first mixed number to improper fraction,

.

We multiply out to obtain,

cubic units.

We need to determine the volume of the cube of side length,

units.

The volume of a cube is given by,

This implies that,

This gives us,

cubic units.

We now divide the volume of the right rectangular prism by the volume of the cube to determine the number of cubes required.

We simplify to get,

This implies that,

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

yes

step-by-step explanation:

yes