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Rates of change and differential equations — Question 287

Original QCE Vault practice · 6 marks

Q287 · Practice questionTechnology-freeSimple familiar6 marks

QUESTION 287 (6 marks)

A tank is an inverted square-based pyramid, 6 m deep with top side length 4 m. Water enters at 8 m3^3/min. The water depth h and water-surface side length s satisfy the same similarity ratio as the full tank. A central vertical cross-section is supplied.
Question 140 stimulus; see the question for exact data and required construction.
a)
Express s and the water volume V in terms of h. Use V=13s2hV=\frac13s^2h.
[2 marks]
b)
Determine dh/dtdh/dt when h=3 m.
[2 marks]
c)
On the blank axes, sketch dh/dtdh/dt as a function of h for 0<h≤60<h\le6. Label its value at h=3 and describe its behaviour near h=0.
[2 marks]
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