Step-by-step solution-:
The Given that:
x=\frac{3}{2\tan{(\theta)}}The Average Speed is:
\frac{dx}{dt}=650~km/hRecall The Chain Rule:
\frac{dx}{dt}=\frac{dx}{d\theta}\cdot \frac{d\theta}{dt}Let be y :
y=\frac{d\theta}{dt} Substitute the
\frac{d\theta}{dt}=y, \theta=\frac{\pi}{3}, {\frac{dx}{d\theta}=-\frac{3}{2\sin^{2}{(\theta)}}}into the above:
\textcolor{primary}{650}=-\frac{3}{2\sin^{2}{\textcolor{secondary}{(\frac{\pi}{3})}}}\cdot \textcolor{tertiary}{y}After simplifying we get,
Therefore, The value of y is:
y=-325~radian ~per~hour
Convert the radian per hour to radian per second:
y=-(325\cdot \frac{1}{3600})~radian ~per~secondConvert the radian per hour to degrees per second
Recall the Converting Degrees and Radians:
Convert radian measure into degrees,
y=-(325\cdot \frac{1}{3600}\cdot \frac{180^{\circ}}{\pi})~degrees ~per~secondAfter simplifying we get,
Therefore, The value of y is:
y\approx-5
Rate is decreased by 5~degrees ~per~second:
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