$\bf \textit{sum of an infinite geometric serie}\\\\
\stackrel{for~~|r|\ \textless \ 1}{S=\sum\limits_{i=0}^{\infty}~a_1r^i\implies \cfrac{a_1}{1-r}}\qquad 
\begin{cases}
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=42\\
r=\frac{3}{4}
\end{cases}
\\\\\\
S=\cfrac{42}{1-\frac{3}{4}}\implies S=\cfrac{42}{\frac{1}{4}}\implies S=164$

bearing in mind that, the geometric sequence is "convergent" only when |r|<1, or namely "r" is a fraction between 0 and 1.

3 0

3 years ago

If you look at a state map with a representative fraction scale of 1:500,000; the straight-line distance between two cities is e

Leya [2.2K]

Answer:

Step-by-step explanation:

The scale factor is given as 1:500,000

i.e. original 500,000 is represented as 1 inch in the map

Hence if 12.7 inches on the map, this is a question of direct variation

So actual distance = 12.7(500000) = 6350000

5 0

3 years ago

The product of five times p and seven times q is

enot [183]

Answer:

Step-by-step explanation:

(5p)(7q)=35pq

7 0

3 years ago

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