솔루션피아

$$ \begin{cases} t &= 0.50\ut{min}\\ v_{C0} &= 15\ut{km/h}\\ v_{C1} &= 45\ut{km/h}\\ v_{B0} &= 0\\ v_{B1} &= 30\ut{km/h}\\ \end{cases} $$ $$ \begin{aligned} v&=v_0+at,\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} a&=\frac{v-v_0}{t}\\ &=\frac{(45\ut{km/h})-(15\ut{km/h})}{0.50\ut{min}}\cdot\frac{60\ut{min}}{1\ut{h}} \\ &=3600\ut{km/h^2}\\ &=3600\ut{km/h^2}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\..

$$ \begin{cases} v_0 &= 3.70\times10^5\ut{m/s}\\ L &= 2.30\ut{cm}\\ v &= 4.40\times10^6\ut{m/s} \end{cases} $$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2,\\ \end{aligned} $$ $$ \begin{aligned} a&=\frac{(4.40\times10^6\ut{m/s})^2-{(3.70\times10^5\ut{m/s})}^2}{2(2.30\ut{cm})}\cdot\frac{100\ut{cm}}{1\ut{m}} \\ &=\frac{9611550000000000}{23}\ut{m/s^2}\\ &\approx4.1789347826086956\times 10^{14}\ut{m/s^2}\\ &..

풀이자주 : 문제의 유효숫자가 애매하여 다양하게 표현했습니다. $$ \begin{cases} g &=9.80665\ut{m/s^2}\\ H &=4000\ut{m}\\ v_0 &= 0 \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2,\\ 2(-g)(-H)&=v^2\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{2gH}\\ &=\sqrt{2(9.80665\ut{m/s^2})(4000\ut{m})}\\ &=\sqrt{\frac{392266}{5}}\ut{m/s}\\ &\approx 280.0949838893942\ut{m/s}\\ &\approx 2.801\times10^2\ut{m/s}\\ &\approx 2..

풀이에 필요한 정보가 너무 부족하여 고양이의 질량과 구성성분비는 임의로 정했습니다. $$ \begin{cases} \text{Cat} &= 5\ut{kg}\\ 1\ut{mol}&=6.02\times10^{23}\\ 1\ut{u}&=1\ut{g/mol} \end{cases} $$ $$ \begin{cases} O : 70\ut{\%}\\ C : 20\ut{\%}\\ H : 10\ut{\%}\\ \end{cases} $$ $$ \begin{cases} m_O &= 16\ut{u}\\ m_C &= 12\ut{u}\\ m_H &= 1.0\ut{u}\\ \end{cases} $$ $$ \begin{cases} M_O &= 5\ut{kg}\cdot0.7=3.5\ut{kg}\\ M_C &= 5\ut{kg}\cdot0..

$$ \begin{aligned} \Ans&=0.257\ut{kg/day}\\ &=0.257\ut{kg/day}\cdot\frac{10^6\ut{mg}}{1\ut{kg}}\cdot\frac{1\ut{day}}{24\ut{h}}\cdot\frac{1\ut{h}}{60\ut{min}} \\ &=\frac{6425}{36}\ut{mg/min}\\ &\approx178.47222222222223\ut{mg/min}\\ &\approx178\ut{mg/min}\\ \end{aligned} $$

$$ \begin{cases} 43\ut{cm}

$$ \begin{cases} V&=40\ut{cm}\times40\ut{cm}\times26\ut{cm} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} V&=41600\ut{cm^3}\\ &=41.6\ut{L}\\ &=41.6\ut{L}\cdot\frac{16\ut{bottle}}{11.356\ut{L}}\\ &=\frac{166400}{2839}\ut{bottle} \approx58.61218738992603\ut{bottle}\\ &=\(2\cdot20+16+2+\frac{1738}{2839}\)\ut{bottle}\\ &=2\ut{nebuchadnezzar}+1\ut{balthazar}+1\ut{magnum}+\frac{1738}{2839}\ut{bottle} \..

$$ \begin{cases} 1\ut{mol}&=6.02\times10^{23}\\ 1\ut{u}&=1\ut{g/mol}\\ \end{cases} $$ $$ \begin{aligned} \Ans&={M\over N}\\ &={68\ut{g}\over 6.8\ut{mol}}\\ &=10\ut{g/mol}\\ &=10\ut{u} \end{aligned} $$

$$ \begin{cases} \rho&=40\ut{mi/gal}\\ 1\ut{U.K.~gal}&=4.546~090~0\ut{L}\\ 1\ut{U.S.~gal}&=3.785~411~8\ut{L}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Ans&={1230\ut{mi}\over40\ut{mi/U.S.~gal}}\\ &={123\over4}\ut{U.S.~gal}\\ &={123\over4}\ut{U.S.~gal}\cdot{3.785~411~8\ut{L}\over1\ut{U.S.~gal}}\\ &=\frac{2~328~028~257}{20~000~000}\ut{L}\\ &\approx116.401~412~85\ut{L}\\ &\approx1.2\times10^2\..

$$ \begin{cases} 1\ut{ken}&=1.97\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \frac{1\ut{ken^2}}{1\ut{m^2}}&=\(\frac{1\ut{ken}}{1\ut{m}}\)^2\\ &=\(\frac{1.97\ut{m}}{1\ut{m}}\)^2\\ &=\frac{38809}{10000}\\ &\approx \frac{388}{100}\\&\approx \frac{97}{25}\\ \end{aligned} $$ $$1\ut{ken^2}:1\ut{m^2}\approx 97:25 $$ $$\ab{b}$$ $$ \begin{aligned} \frac{1\ut{ken^3}}{1\ut{m^3}}&=\(\frac{1\ut{ken}..