Tyler has two cube-shaped storage spaces in his apartment building, one large and one small. The small storage space has a volume of 12 ft. Tyler wants to know the total
volume of both storage spaces.
s = length (ft) of one side of the large storage space
• Which expression represents the total
volume of the two storage spaces?
8
12 ft3
38 +12
(s +12)
S
8
83 +12
$3 +12

s³ + 12

Step-by-step explanation:

The volume of a cube is gotten by using the formula:

Volume of cube = (side)³

Since there are two cubes. The volume of the bug cube will be:

= s × s × s = s³

Volume of small cube = 12ft³

Therefore, the expression represents the total volume of the two storage spaces will be:

= s³ + 12

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.