2 years ago

Independent or dependent {-3x+y=4 {X-1/3y=1

Mathematics

1 answer:

Lemur [1.5K]2 years ago

5 0

Dependent since det =0

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2 years ago

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3 years ago

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notsponge [240]

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2 years ago

Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

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so as you can see the common ratio is 2, and the first term is 1/2,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}$

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3 years ago

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