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376.99 cm^3 or 120π cm^3

Step-by-step explanation:

The volume of a cone is 1/3(B*h) where B is the base area and h is height.

The base of a cone is a circle.

Area of a circle=πr^2

Area of the circle=π6^2

Area of the circle=36π

Plug it into the formula for the volume:

V=1/3(36π*10)

V=1/3(360π)

V=120π

V=376.99

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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.