4 years ago

A teenager can wash 2

Mathematics

1 answer:

leva [86]4 years ago

3 0

2 * M = X
M = to minutes
x = to how many tables washes

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How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160

Marina CMI [18]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=3\\
S_n=160
\end{cases}$

$\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
\\\\\\
160=2(3^n-1)\implies \cfrac{160}{2}=3^n-1\implies 80=3^n-1
\\\\\\
81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^4=3^n\implies 4=n$

3 0

3 years ago

How could I get rid of the 3 shown in equation 1?

Tems11 [23]

Answer:

Step-by-step explanation:

3 log 2+log (x-4)=log 2³+log (x-4)=log 8+log (x-4)=log 8(x-4)

8 0

3 years ago

Need help solving for Y

vampirchik [111]

Cos35= y/15
y= 15cos35
y= 12.3 cm