Quick question about the answer to 2005 maths paper (1 Viewer)

[blackops23]

2005 2u mathematics paper, q6b

A tank initially holds 3600 litres of water. The water drains from the bottom of
the tank. The tank takes 60 minutes to empty.
A mathematical model predicts that the volume, V litres, of water that will
remain in the tank after t minutes is given by

V = 3600*(1- t/60)^2 , where 0(<)t(<)60

At what rate does the model predict that the water will drain from the
tank after twenty minutes?

------

On pasthsc.com.au, it says the answer is 80L/min
I got 40L/min
I mean after 20minutes, there is 1600L left, which MUST BE DRAINED IN 40 MINUTES, so isn't it 40L/min??

Or am I doing something wrong?


Also: At what time does the model predict that the water will drain from the tank at its fastest rate?
How do I calculate this?

 

[bored of fail 1]

dV/dt = 2 x 3600 ( 1- t/60 ) x -1/60 = -120 ( 1 -t/60 ) = -120 ( 1 - 20/60 ) = 2/3 x -120 = -80

decreasing at 80L/min

 

[NewiJapper]

^beat me to it.

 

[bored of fail 1]

At what time does the model predict that the water will drain from the tank at its fastest rate?
How do I calculate this?


mmm we want to know the FASTEST ( ie largest ) value of rate , what would be do ....

 

[blackops23]

At what time does the model predict that the water will drain from the tank at its fastest rate?
How do I calculate this?


mmm we want to know the FASTEST ( ie largest ) value of rate , what would be do ....

my bad

 

[Aindan]

On pasthsc.com.au, it says the answer is 80L/min
I got 40L/min
I mean after 20minutes, there is 1600L left, which MUST BE DRAINED IN 40 MINUTES, so isn't it 40L/min??

Or am I doing something wrong?

Well you see, the water does not drain at a uniform rate. It drains the most initially then gradually drains less and less. That is why in the first 20 minutes , 2000 L has drained which equivilates to 100L per minute on average in the first 20 minutes. Don't do that method to answers questions because it only works when it drops at the same rate all times, try and use the official method.

 

[blackops23]

dV/dt = 2 x 3600 ( 1- t/60 ) x -1/60 = -120 ( 1 -t/60 ) = -120 ( 1 - 20/60 ) = 2/3 x -120 = -80

decreasing at 80L/min

can sum1 add a few words here as well?, so you find the derivate, sub t=20 in, to find -80, how does that fit in with the question?

 

[bored of fail 1]

can sum1 add a few words here as well?, so you find the derivate, sub t=20 in, to find -80, how does that fit in with the question?

wtf, drop to general maths immediately, all the way from 4unit to general, tommorow u must do it

 

[MrBrightside]

wtf, drop to general maths immediately, all the way from 4unit to general, tommorow u must do it

using normal school standard protocols of changing a subject it would take 4 weeks at minimum to successfully change your subject. and you would have to convince the subject coordinator why you would want to do so and get a sheet sgined by every teacher / your parents etc

 

[AAEldar]

using normal school standard protocols of changing a subject it would take 4 weeks at minimum to successfully change your subject. and you would have to convince the subject coordinator why you would want to do so and get a sheet sgined by every teacher / your parents etc

I could do it in a day.

 

[Studentleader]

I could do it in a day.

could ya rly m8