A right rectangular prism has edges measuring 3/4 inch, 1 inch, and 1/4 inch. How many cubes with side lengths of 1/4 would be needed to fill the prism.

The number of cubes needed = 12

Step-by-step explanation:

To know the number of cubes that will be needed to fill the prism, we need to divide the the volume of the right rectangular prism by the volume of the cube.

Mathematically, the volume of the right rectangular prism can be calculated using the formula;

V = whl

where w is the width, h is the height and l is the length.

Plugging the values we have in the question for the right rectangular prism, we have;

V = 3/4 * 1 * 1/4 = 3/16 inch^3

The volume of the cube can be calculated using the formula L^3 where L is the side length

V = 1/4 * 1/4 * 1/4 = 1/64 inch^3

The number of cubes needed to fill the prism is thus;

(3/16) ÷ (1/64) = 3/16 * 64/1 = 3 * 4 = 12

853.3

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for