A cylindrical container can hold about 1,256 cubic inches of water. The diameter of the cylinder is 10 inches long. Approximate the height if the cylinder to the nearest inch . Use 3.14 to approximate the value of _.

ANSWER 16 in

see explanation

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ← r is the radius and h the height

Here diameter = 10, thus r = 10 ÷ 2 = 5 and V = 1256, thus

π × 5² × h = 1256, that is

25πh = 1256 ( divide both sides by 25π )

h = = 16 in

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.