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Mathematics

1 answer:

Vlada [557]3 years ago

3 0

The side of the square is 4 cm since 4x4= 16

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One liter of paint covers 100 square feet. How many gallons of paint does it take to cover a room whose walls have an area of 80

mezya [45]

1 gallon is 3.78 L
100 sq feet needs 1 L
800 sq feet needs x

100/800 = 1/x
100x = 800
x = 800/100
x = 8 L

If you use the fact that 4 L = 1 gallon then you need 2 gallons of paint. I you use the more accurate 3.78 L then
1 gallon = 3.78 L
x gallon = 8 L

3.78 x = 8*1
x = 8/3.78
x = 2.12 gallons.

I guess you could say that 1 gallon and 1 L would do you.

8 0

3 years ago

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

Roman55 [17]

$\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...$

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

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