jmwmarshall

12.07.2019 •

Mathematics

Select the correct answer.
in the diagram, quadrilateral lmno is a parallelogram. what is the length of ?
a.
6
b.
5.66
c.
5.39
d.
2.24

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Ответ:

codycollier

07.03.2021

Mathematics

The rebound of the ball from the height is an illustration of a geometric series

The total vertical distance at the 10th rebound is 60.352 feetThe first five terms of the sum are 16, 12, 9, 6.75 and 5.0625

(a) The total vertical distance

The given parameters are:

$\mathbf{a = 16}$ -- the first term

$\mathbf{r = \frac 34}$ -- the common ratio

$\mathbf{n = 10}$ -- number of terms

The total vertical distance when it strikes for the 10th time is the sum of nth terms of the geometric series.

So, we have:

$\mathbf{S_n = \frac{a(1 - r^n)}{1- r}}$

Substitute values for (a), (r) and n

$\mathbf{S_{10} = \frac{16(1 - 3/4^{10)}}{1- 3/4}}$

Simplify

$\mathbf{S_{10} = \frac{16(0.943)}{0.25}}$

$\mathbf{S_{10} = 60.352}$

Hence, the total vertical distance at the 10th rebound is 60.352 feet

(b) The first five terms of this sum

The nth term of a geometric series is:

$\mathbf{T_n = ar^{n-1}}$

So, we have:

$\mathbf{T_1 = 16}$

$\mathbf{T_2 = 16 * 3/4 = 12}$

$\mathbf{T_3 = 12 * 3/4 = 9}$

$\mathbf{T_4 = 9 * 3/4 = 6.75}$

$\mathbf{T_5 = 6.75 * 3/4 = 5.0625}$

Hence, the first five terms of the sum are 16, 12, 9, 6.75 and 5.0625

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Select the correct answer. in the diagram, quadrilateral lmno is a parallelogram. what is the length of ? a. 6 b. 5.66 c. 5.39 d. 2.24