Simplify the expression \[\frac{6}{\sqrt{36} + \sqrt{27}} + \frac{6}{\sqrt{27} + \sqrt{18}} + \frac{6}{\sqrt{18} + \sqrt{9}}.\]
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Answer:
A
Step-by-step explanation:
This is exponential decay; the height of the ball is decreasing exponentially with each successive drop. It's not going down at a steady rate. If it was, this would be linear. But gravity doesn't work on things that way. If the ball was thrown up into the air, it would be parabolic; if the ball is dropped, the bounces are exponentially dropping in height. The form of this equation is
, or in our case:
, where
a is the initial height of the ball and
b is the decimal amount the bounce decreases each time. For us:
a = 1.5 and
b = .74
Filling in,
If ww want the height of the 6th bounce, n = 6. Filling that into the equation we already wrote for our model:
which of course simplifies to
which simplifies to
So the height of the ball is that product.
A(6) = .33 cm
A is your answer