Can you confirm that I have done this correct please?

getinthere

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Oct 26, 2014
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Hi,

I have been given a question involving calculus, I have answered this question as I feel is correct, but would like someone to verify this and point out any errors I may have made.

The question:

When a heated object is cooling down, the rate of change of the object’s internal temperature T(t) is proportional to S (t) -T(t), where S (t) is the temperature of the surroundings in which the object is immersed.

a) Form a differential equation that describes the situation above, using k for the constant of proportionality.

A ball made from a specialised metal alloy is being tested to determine some of its material properties. As part of the test, the ball is heated throughout to 200°C and then immediately immersed into a large pool of temperature controlled water, Whose temperature obeys the formula S(t) = 15e^-5t + 5. For this specific ball, k = 0.5. Let t by the time in hours after the ball has started to cool down, so that T(0) = 200.

b) Solve the differential equation in part (a) to iind the particular solution T(t).

My answer is attached, thank you.

John
 

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For those who (like me) have difficulty with small sideways images, here is a rotated and clarified version:

attachment.php
 

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Thank you for doing that for me, but am I correct or do I need to redo it? If so where did I start to go wrong?

Thank you
 
Thank you for all the input, 117 views and not one person can say yes or no as to whether I had answered a maths question right on a maths forum, the only input I received was to turn my attachment around, well done you.

Turns out it was correct except a silly mistake with the value of C which should be 590/3, I had done correct workings just put wrong value.

Any way my HND course is now complete so will not require the excellent help that I have received through this forum, cannot thank you enough.

John

Ps drop the help from the site name as it's misleading.
 
Feel free to calm down. We have volunteers. They come when they can. Has anyone charged you anything?

Very early on, you dropped from three terms to only two terms. Magically, though, the third term came back.

We don't come here to work problems and prove that we can do them. You showed very clean and organized work. No one had a particular objection to it. Perhaps you should learn confidence from this experience, rather than add it to your lifetime supply of anger. No?
 
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