Two boxes have the same volume. one box has a base that is 2 inches by 2 inches. the other box has a base that is 4 inches by 4 inches.
how many times as tall is the box with the smaller base?

4 times as tall.

Step-by-step explanation:

Volume of the box with the smaller base = 2*2* h1 = 4h1 where h1 is its height.

Similarly the volume of the larger base box =  4*4 * h2 = 16h2 with height h2.

So the ratio of their volumes is  16h2 / 4h1 = 4h2 / h1.

Now the volumes are equal so 4h2 = h1.

Therefore   h2 = h1/4  so h1 = 4h2.

The box with the smaller base is 4 times as tall as the other box.

henry ordered 5 large pizzas

step-by-step explanation:

sorry no step by step

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.