MATH100 December 2018
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 (a) • Q11 (b) •
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
|
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.
|
[show]Hint 2
|
To solve a differential equation of the form
,
we can make the substitution .
|
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
- If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
|
[show]Solution
|
We denote by the temperature function (with respect to time
, which is measured in minutes, while the temperature is measured
in degrees Celsius) for the soda can.
The initial time is when
we made the first reading of the temperature of the soda can (i.e., 1 p.m.). So, we
know that and .
According to Newton's Law of Cooling, we have the following equation:
for some negative constant . We let ; then
and therefore, we have
,
which means that , where
.
So, and therefore, .
Because , we get that
and so, ,
which means that and so,
.
Thus, and we need to find
the time when the can was put in the refrigerator, i.e., when
; note that will be negative since the
soda can was placed in the refrigerator prior to time ,
represented by 1 p.m. So, we have
and thus , which yields
and so,
and so,
.
Therefore, the soda can was placed in the refrigerator
minutes prior to 1 p.m.
|
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag
|
Math Learning Centre
- A space to study math together.
- Free math graduate and undergraduate TA support.
- Mon - Fri: 12 pm - 5 pm in MATH 102 and 5 pm - 7 pm online through Canvas.
|