Eric Nicholas K's answer to Kathy's Secondary 4 A Maths Singapore question.
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Q8
Kathy, this topic is basically understanding how things change with time, since rate is related to the time t. We use chain rule formulas involving t, such as dV/dt = dV/dh dh/dt to solve such questions.
The steps to solve this question are as follows.
1. Extract out useful information and transform them into words. Here, the depth increases at 2 cm/s, so we transform it to dh/dt = 2 cm/s.
2. We find out what our wanted quantity is. Here, it’s dV/dt.
3. We express dV/dt in terms of dV, dh and dt. Here, it’s dV/dt = dV/dh dh/dt (think of this as “cross multiplication”), so we need to find out what dV/dh is. It’s the rate of change of V with respect to h, so we need to know what V is in terms of h. It’s given in this question. At other times, you need to form your own equation (such as area of a circle A = #r2).
4. Finally, multiply them out to get the value.
Kathy, this topic is basically understanding how things change with time, since rate is related to the time t. We use chain rule formulas involving t, such as dV/dt = dV/dh dh/dt to solve such questions.
The steps to solve this question are as follows.
1. Extract out useful information and transform them into words. Here, the depth increases at 2 cm/s, so we transform it to dh/dt = 2 cm/s.
2. We find out what our wanted quantity is. Here, it’s dV/dt.
3. We express dV/dt in terms of dV, dh and dt. Here, it’s dV/dt = dV/dh dh/dt (think of this as “cross multiplication”), so we need to find out what dV/dh is. It’s the rate of change of V with respect to h, so we need to know what V is in terms of h. It’s given in this question. At other times, you need to form your own equation (such as area of a circle A = #r2).
4. Finally, multiply them out to get the value.
Date Posted:
4 years ago
Kathy, my phone is ok already so I can continue to help you do some questions.
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