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3 years ago

Someone, please help I'm confused.

Mathematics

1 answer:

djyliett [7]3 years ago

8 0

Answer:

The highest rate of birds is during the years 4 to 3

(remember that the lowest digit of number of negative is the highest and the highest is the lowest)

Step-by-step explanation:

Rate of Changes:

1 to 2: 5080.86 - 5238/ 2 - 1

= -157.14/1

= (convert to decimal) -157.1

2 to 3: 4928.43 - 5080.86/ 3 - 2

= -152.43/ 1

= -152.43

3 to 4: 4780.58 - 4928.43/ 4 - 3

= -147.85/ 1

= -147.85

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3 years ago

Find S15 for the geometric series 72 + 12 + 2 + +…

Sedbober [7]

$S_{15}=72+12+\cdots+\dfrac1{181398528}+\dfrac1{1088391168}$
$S_{15}=72\left(\dfrac16\right)^0+72\left(\dfrac16\right)^1+\cdots+72\left(\dfrac16\right)^{13}+72\left(\dfrac16\right)^{14}$
$S_{15}=72\displaystyle\sum_{i=1}^{15}\left(\frac16\right)^{i-1}$

$\dfrac16S_{15}=72\displaystyle\sum_{i=1}^{15}\left(\frac16\right)^i$

$\implies S_{15}-\dfrac16S_{15}=72\displaystyle\sum_{i=1}^{15}\bigg(\left(\dfrac16\right)^{i-1}-\left(\dfrac16\right)^i\bigg)$
$\dfrac56S_{15}=72\bigg(\left(1-\dfrac16\right)+\left(\dfrac16-\dfrac1{6^2}\right)+\cdots+\left(\dfrac1{6^{13}}-\dfrac1{6^{14}}\right)+\left(\dfrac1{6^{14}}-\dfrac1{6^{15}}\right)\bigg)$
$\dfrac56S_{15}=72\left(1-\dfrac1{6^{15}}\right)$
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3 years ago