VCE Specialist 3/4 Question Thread!

[saba.ay]

The height of the water in the vase goes from 30cm to 0cm.



Not sure if correct, could probably use a check.

That's what I got too, but the answer was the following:



I get the limits of 0-25 because initially the height is 25.

But, I don't understand where the 12 comes from? :/

[09Ti08]

Umm, I think you need to convert 15cm3/s into 900cm3/min. The unit of time in the question is minutes. I did everything again and got your answer.

[Daenerys Targaryen]

Okay homies!!

The water in a hot water tank cools at a rate which is proportional to where T*C is the temperature of the water at t minutes and the temperature of the surrounding air. When T is 60 the water is cooling at 1*C per minute.
When switched on the heater supplies sufficient heat to raise the temperature by 2*C each minute (neglecting heat loss by cooling). If T=20 when the heater is switched on and :

Construct a differential equation for as a function of T (heating and cooling are both taking place)


Cheers

[SocialRhubarb]

From cooling:







From heating:



Together:

[Daenerys Targaryen]

Together:

How did you know whether to add/subtract here?

Soz

[09Ti08]

For the cooling process: Temperature is decreasing, so dT/dt<0. Another way to think about it is if you let T to be T=at+b, then for T to decrease as t increases, dT/dt<0. This applies to any function whose value is decreasing.

[Daenerys Targaryen]

For the cooling process: Temperature is decreasing, so dT/dt<0. Another way to think about it is if you let T to be T=at+b, then for T to decrease as t increases, dT/dt<0. This applies to any function whose value is decreasing.

Sorry, but that didn't quite exactly answer my question. Appreciate the help but doesnt help... Sorry

Together:

Wanted to know why it was heating process + cooling process

[SocialRhubarb]

The heating system is providing a constant rate of heating, and it relates to the amount of heat the system is gaining.

The cooling system is acting independently of the heating system, and relates to the amount of heat that the system is losing.

The net gain in temperature is equal to the amount of heat that the system has gained minus the amount of heat that the system has lost.

While the two systems do act relatively independently of each other, they both affect the same variable: temperature. So, since we're trying to find an expression for the change in temperature with respect to time, we have to take into account both the cooling and the heating, as they both affect the temperature.

As for why we add them, they both have the same units, and if we're trying to find the net change in temperature, we take the difference between the rate of heat gain and heat loss, or the 'sum' of the the gains and the losses.

[barydos]

Hey, just got a quick question regarding kinematics:

Spoiler

Just not sure how we suddenly jumped to (on the line after "Also")
Where did it come from?

Thanks

[lzxnl]

d(1/2 v^2)/dx = d(1/2 v^2)/dv * dv/dx = v*dv/dx

[Alwin]

Hey, just got a quick question regarding kinematics:

Spoiler

Just not sure how we suddenly jumped to (on the line after "Also")
Where did it come from?

Thanks

Thats one way of proving it

EDIT: lol nliu, I think you typed exactly what was in the the pic he attached haha. But its exact same to my "proof", just reversed

[barydos]

Thats one way of proving it

EDIT: lol nliu, I think you typed exactly what was in the the pic he attached haha. But its exact same to my "proof", just reversed

Thanks a lot!!!
Also thanks nliu i guess haha

[Limista]

Anyone know how to antidiff  4x/5πsin(x/5) by hand? I don't know if this is not do-able, or if I'm just having a major mind blank right now.

[lzxnl]

Do you mean...

Or did you want the sine function in the denominator? If you want it in the denominator, it can't be integrated. I can integrate it in the form given though. Differentiate x*sin(x/5) and see if you can use that result.

[Limista]

Do you mean...

Or did you want the sine function in the denominator? If you want it in the denominator, it can't be integrated. I can integrate it in the form given though. Differentiate x*sin(x/5) and see if you can use that result.

Yeah sine was supposed to be in numerator. Integration by recognition. Whhyy did I not think of that? Thanks again