10 The equation of a curve is \(\mathrm { y } = ( 5 - 2 \mathrm { x } ) ^ { \frac { 3 } { 2 } } + 5\) for \(x < \frac { 5 } { 2 }\).
- A point \(P\) is moving along the curve in such a way that the \(y\)-coordinate of point \(P\) is decreasing at 5 units per second.
Find the rate at which the \(x\)-coordinate of point \(P\) is increasing when \(y = 32\).
- Point \(A\) on the curve has \(y\)-coordinate 32. Point \(B\) on the curve is such that the gradient of the curve at \(B\) is - 3 .
Find the equation of the perpendicular bisector of \(A B\). Give your answer in the form \(\mathrm { ax } + \mathrm { by } + \mathrm { c } = 0\), where \(a , b\) and \(c\) are integers.
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