Given that $2x-{{y}^{2}}-3xy=1$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ a

Question

Given that $2x-{{y}^{2}}-3xy=1$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.[4] For the curve with equation $2x-{{y}^{2}}-3xy=1$, find the coordinates of the points on the curve at which the tangent is parallel to the $y$-axis.[4] The volume of water that can be contained in a specific bowl is given by $V=\frac{\pi }{3}\left[ 9{{x}^{2}}-{{x}^{3}} \right]$, where $x$ cm is the depth of the water in the bowl at time $t$ seconds. Water is poured in at the constant rate of $4$cm$^{3}$s$^{-1}$ and leaks out from a hole at the bottom of the bowl at a constant rate of $k$cm$^{3}$s$^{-1}$ . Given that the depth of water is rising at a rate of $\frac{1}{9\pi }$cm s$^{-1}$ when the depth is $3$ cm, find the value of $k$.[3]

Accepted Answer

$k = 3$

2024 MI PRU2 P1 Q10

2024 MI PRU2 P1 Q10

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