7 A water tank of height 1 m has a square base 2 m x 2 m. When a tap at its base is opened, the water flows out at a rate proportional to the square root of the depth of the water at any given time. Suppose the depth of the water is h m, and V is the volume of water remaining in the tank after t minutes. a Write down a differential equation involving dV and h to model this situation. dt b Explain why V = 4h m3 at time t, then use the chain rule to write down a differential equation involving dh and h only. dt C The tank is initially full. When the tap is opened, the water level drops by 19 cm in 2 minutes Findd the t kes for the tonk to em

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7 A water tank of height 1 m has a square base 2 m x 2 m. When a tap at its base is opened,
the water flows out at a rate proportional to the square root of the depth of the water at any
given time. Suppose the depth of the water is h m, and V is the volume of water remaining in
the tank aftert minutes.
dV
and h to model this situation.
dt
a Write down a differential equation involving
6 Explain why V = 4h m³ at time t, then use the chain rule to write down a differential
equation involving
dh
and h only.
dt
c The tank is initially full. When the tap is opened, the water level drops by 19 cm in
2 minutes. Find the time it takes for the tank to empty.
Transcribed Image Text:7 A water tank of height 1 m has a square base 2 m x 2 m. When a tap at its base is opened, the water flows out at a rate proportional to the square root of the depth of the water at any given time. Suppose the depth of the water is h m, and V is the volume of water remaining in the tank aftert minutes. dV and h to model this situation. dt a Write down a differential equation involving 6 Explain why V = 4h m³ at time t, then use the chain rule to write down a differential equation involving dh and h only. dt c The tank is initially full. When the tap is opened, the water level drops by 19 cm in 2 minutes. Find the time it takes for the tank to empty.
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