Figure 1 shows a paperweight made from a hollow hemisphere and a hollow cone. The paperweight contains sand so that the sand exa
ctly fills the hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 15cm and the volume of the cone is 180π cm3 Figure 2 below shows the paperweight after it has been turned upside down. Diagram NOT accurately drawn h cm Figure 2 The height of the sand in the cone is h cm. Find, to 3 significant figures, the value of h.
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Answer:
The height of a bouncing ball is defined by .
Step-by-step explanation:
According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:
,
,
(1)
Where:
- Height reached by the ball on the first bounce, measured in feet.
- Decrease rate, no unit.
- Number of bounces, no unit.
- Height reached by the ball on the n-th bounce, measured in feet.
The decrease rate is the ratio between heights of two consecutive bounces, that is:
(2)
Where is the height reached by the ball on the second bounce, measured in feet.
If we know that and
, then the expression for the height of the bouncing ball is:
The height of a bouncing ball is defined by .