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Mandarinka [93]
3 years ago
6

If a rectangle has an area of 64 square units and a length of 16 units, what is its width? If necessary, round your answer to tw

o decimal places.
Mathematics
1 answer:
sveta [45]3 years ago
7 0
The formula for finding area of a rectangle is a=lw.

Write what is given
Area is 64.
Length if 16.
Width is unknown.
Therefore the equation would look like this:
64=16*w
Now to solve for w.
Divide 16 both sides.
64/16 is 4. Therefore:
w=4
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The height h(n) of a bouncing ball is an exponential function of the number n of bounces.
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Answer:

The height of a bouncing ball is defined by h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}.

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:

h = h_{o}\cdot r^{n-1}, n \in \mathbb{N}, 0 < r < 1 (1)

Where:

h_{o} - Height reached by the ball on the first bounce, measured in feet.

r - Decrease rate, no unit.

n - Number of bounces, no unit.

h - 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:

r = \frac{h_{1}}{h_{o}} (2)

Where h_{1} is the height reached by the ball on the second bounce, measured in feet.

If we know that h_{o} = 6\,ft and h_{1} = 4\,ft, then the expression for the height of the bouncing ball is:

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