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Helga [31]
4 years ago
12

You increase the size of a paper by 30% then you decrease it by 30% what is the size of the paper now

Mathematics
1 answer:
polet [3.4K]4 years ago
7 0
I'm assuming that this is applying to the linear dimensions. Let's say the paper is 10 inches by 10 inches

The new paper will be 13 inches by 13 inches since 
30% of 10 = 0.3*10 = 3, and we add on 3 to 10 to get 13
Another way to see it: 130% of 10 = 1.3*10 = 13

--------------------------------------

Now decrease the paper by 30%
30% of 13 = 0.3*13 = 3.9
13 - 3.9 = 9.1
This is the same as saying 70% of 13 = 0.7*13 = 9.1

The paper is now 9.1 inches by 9.1 inches

As you can see, the paper has not been restored to its original size (10 by 10). The reason why is because 30% of a larger number leads to a bigger decrease than expected. 
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again, let's assume daily compounding means 365 days per year.

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~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &1 \end{cases}

A=10000000\left(1+\frac{0.0212}{365}\right)^{365\cdot 1}\implies A\approx 10214256.88 \\\\\\ \underset{\textit{earned interest amount}}{10214256.88~~ - ~~10000000 ~~ \approx ~~ \boxed{214256.88}}

what's their difference?  well

\stackrel{\textit{compounded daily}}{\approx 214256.88}~~ - ~~\stackrel{\textit{simple interest}}{212000}\implies \boxed{2256.88}

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the volume of the triangular prism can be found with
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Now add the two volumes together for the total volume...

3000+1350 = 4,350 in^3
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