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\frac{\mathrm{d} \mathrm{x}}{\mathrm{dt}}-40 \csc ^{2}(\theta) \frac{\mathrm{d} \theta}{\mathrm{dt}}=-40 \frac{1}{\sin ^{2}(\theta)} \frac{\mathrm{d} \theta}{\mathrm{dt}} \approx-40 \frac{1}{(0.1736)^{2}}(0.0349) \approx-46.3 \, \mathrm{ft} / \mathrm{min}.