A right rectangular prism's edge lengths are 6 inches, 3 inches, and 3 1/2 inches. How many unit cubes with edge lengths of 1/3 inch can fit inside the prism?

1701

Step-by-step explanation:

To know this, we must calculate the volume of each one and then divide the volume of the prism by the volume of the cube, so we will know how many can enter.

The volume of the rectangular prism:

V = a * b * c

a = 6, b = 3 and c = 3 1/2 = 3.5

replacing

V = 6 * 3 * 3.5 = 63

which means the volume of the prism is 63 cubic inches

The cube volume:

v = a ^ 3

a = 1/3

replacing

v = (1/3) ^ 3

v = 0.037037

Which means that the volume of the cube is 0.037037 cubic inches

Now to know how many can enter it would be:

V / v = 63 / 0.037037 = 1701

Which means that up to 1701 cubes with 1/3 inch edges can fit

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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