Maths Quest Question - Integration

[cleo_xo]

I'm really lost on this question any help for any question is really apreciated

[the.watchman]

Integrate the function and use the given information to find c:



Because when t=0, T=10

Therefore:



So

I think you can do the rest yourself

[Whatlol]

I'm really lost on this question any help for any question is really apreciated

Ok so for part a). Since the given function is the rate of change of temperature, integrating this will produce the function of temperature.
                    b). Just simply let the function of temperature equal 17 and then solve for t, (if there is no solution answer is no).
                    c). maximum temperature will occur when the function of the rate of change of temperature is equal to 0, ( you will need to find which is a maximum / minimm). Alternatively, you
                         can solve this problem by using the amplitude of the temperature function ( which is the integral of dT/dt)
                    d). this problem can be solved using the same methods in the previous question.
                    e). this can be found by substituting t=2 and t = 15 into the temperature function (since t is hours after midnight)
                    f). let the temperature function =14.33 and solve for t.

[cleo_xo]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

[Whatlol]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

Oh look at the watchmans post (= he did a much better job than me.

[cleo_xo]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

Oh look at the watchmans post (= he did a much better job than me.

sorry i mean how did he get the first equation??

[the.watchman]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

Ok, it's:

[cleo_xo]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

Ok, it's:

please dont laugh lol why do you multiply it with 12/pi

[the.watchman]

sorry i have a really dumb question, how exactly do you integrate it? i suck at maths

Ok, it's:

please dont laugh lol why do you multiply it with 12/pi

It's like the opposite of the chain rule, you know how you multiply by the constant in front of the t when differentiating?
Well, when anti-differentiating, you do the opposite, so you divide by the constant.

[jasoN-]

Don't let the "complex" fractions get in the way of your thinking process
You should know that , where k is a constant
Apply this to the above, where



Edit: woops misread, editted for fix

[cleo_xo]

Don't let the "complex" fractions get in the way of your thinking process
You should know that , where k is a constant
Apply this to the above, where



Edit: woops misread, editted for fix

thanks heaps!!!!!!!!!!!!!

[cleo_xo]

so im doing question c and i worked out t= 12/pi which is obviously wrong, any help please?

[Whatlol]

so im doing question c and i worked out t= 12/pi which is obviously wrong, any help please?

what value for temperature did you use?

[jasoN-]

Well as we worked out

Using T=10 at t=0, you work out that c=10

You don't need to work much out from here to find the max and min temperatures.
Firstly:

(it would help if you drew out a rough sketch from [0,24]
hence, Max temp = c + a
                        = 10+5
                        = 15



We know



          Min temp = c - a
                       = 10-5
                       = 5



We know



Therefore: Max temp of 15 degrees occurs at 6pm (as t=0 is midnight)
and Min temp of 5 degrees occurs at 6 am

[jasoN-]

Dam, forgot the easier method

Alternatively:
Max temperature indicates the gradient of the Temperature function
Simply let



We know
Hence:
and
and
By subbing these t values into the integrated equations, the max and min temperatures can be identified