Find the product (0.5 n^5 ) ^2 (10 n^7 ) ^3

1 answer:

6 0

$(0.5n^{5})^2 \cdot (10n^{7})^{3} = 0.5^{2} \cdot n^{10} \cdot 1000n^{21} = (\frac{1}{2})^{2} \cdot n^{10} \cdot 1000n^{21} = \frac{1}{4}n^{10} \cdot 1000n^{21} = n^{10} \cdot 250n^{21} = 250n^{31}.$

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Answer with Step-by-step explanation:

The given differential euation is

$\frac{dy}{dx}=(y-5)(y+5)\\\\\frac{dy}{(y-5)(y+5)}=dx\\\\(\frac{A}{y-5}+\frac{B}{y+5})dy=dx\\\\\frac{1}{100}\cdot (\frac{10}{y-5}-\frac{10}{y+5})dy=dx\\\\\frac{1}{100}\cdot \int (\frac{10}{y-5}-\frac{10}{y+5})dy=\int dx\\\\10[ln(y-5)-ln(y+5)]=100x+10c\\\\ln(\frac{y-5}{y+5})=10x+c\\\\\frac{y-5}{y+5}=ke^{10x}$