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\includegraphics[max width=\textwidth, alt={}, center]{b1c4d339-322f-496d-833e-8b2d002d7c48-12_431_547_280_758} A container in the shape of a cuboid has a square base of side \(x\) and a height of ( \(10 - x\) ). It is given that \(x\) varies with time, \(t\), where \(t > 0\). The container decreases in volume at a rate which is inversely proportional to \(t\). When \(t = \frac { 1 } { 10 } , x = \frac { 1 } { 2 }\) and the rate of decrease of \(x\) is \(\frac { 20 } { 37 }\).

1. Show that \(x\) and \(t\) satisfy the differential equation $$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { - 1 } { 2 t \left( 20 x - 3 x ^ { 2 } \right) }$$ \includegraphics[max width=\textwidth, alt={}, center]{b1c4d339-322f-496d-833e-8b2d002d7c48-12_2739_47_123_2001}
2. Solve the differential equation, obtaining an expression for \(t\) in terms of \(x\).