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Home » 81を \( 3^4 \) と書き換えます。 - Simpleprint

81を \( 3^4 \) と書き換えます。 - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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r = \frac{A}{s}
where $A$ is the area of the triangle and $s$ is the semi-perimeter:
s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = 21
Using Heron’s formula for area:
r = \frac{84}{21} = 4
$$Question: What is the largest possible value of $\gcd(a,b)$, if the...
Let $d = \gcd(a,b)$. Then we can write $a = dx$, $b = dy$, where $\gcd...
dx + dy = d(x + y) = 1000 \Rightarrow d \mid 1000
So $d$ must be a divisor of 1000. Also, both $a$ and $b$ must be divis...
To maximize $d$, we look at the largest divisor of 1000 such that $x =...

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-0.5t = \ln\left(\frac{1}{9}\right) = -\ln 9
Solve for \(t\):
t = \frac{-\ln 9}{-0.5} = \frac{\ln 9}{0.5} = 2 \ln 9 = \ln(9^2) = \ln...
Alternatively, express the final result clearly:
t = \frac{\ln 9}{0.5} = 2 \ln 9 = 2 \ln(3^2) = 4 \ln 3
Thus, the time when the population reaches 500 is:
\boxed{2 \ln 9}
Or, simplified numerically in terms of known logs, but the exact form...
\boxed{2\ln 9}
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