\[\boxed{\mathbf{1102.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[C = 2\pi R.\]
\[\textbf{а)}\ R_{1} = 3R \Longrightarrow C_{1} = 2\pi \bullet 3R =\]
\[= 6\pi R:\]
\[\frac{C_{1}}{C} = \frac{6\pi R}{2\pi R} = 3 - увеличится\ \]
\[в\ три\ раза;\]
\[\textbf{б)}\ R_{1} = \frac{R}{2} \Longrightarrow C_{1} = 2\pi \bullet \frac{R}{2} = \pi R:\]
\[\frac{C_{1}}{C} = \frac{\text{πR}}{2\pi R} = \frac{1}{2} - уменьшится\ \]
\[в\ два\ раза;\]
\[\textbf{в)}\ R_{1} = kR \Longrightarrow C_{1} = 2\pi \bullet kR =\]
\[= 2k\pi R:\]
\[\frac{C_{1}}{C} = \frac{2k\pi R}{2\pi R} = k - увеличится\ \]
\[в\ k\ раз.\]
\[\textbf{г)}\ R_{1} = \frac{R}{k} \Longrightarrow C_{1} = 2\pi \bullet \frac{R}{k} = \frac{2}{k}\pi R:\]
\[\frac{C_{1}}{C} = \frac{2\pi R}{k \bullet 2\pi R} = \frac{1}{k} - уменьшится\ \]
\[в\ \text{k\ }раз.\]