Math*2270, Fall 2012
Due Wednesday, October 17 in class
▯ Ensure that your name and ID Number are clearly printed on the front page.
▯ You are encouraged to work with your friends to complete the assignment, but please write
up your ▯nal solutions on your own.
▯ Submit your assignment in class on or before the due date.
▯ This assignment carries a weight of 4% of your ▯nal grade. Late submissions will be given a
1. Find the general solution for the following Bernoulli equation:
x + tan(t)x = x sec (t)
2. Reduced visibility caused by particulate matter in the atmosphere is a problem,
commonly referred to as haze. Diminishing visibility with distance can be quanti▯ed
by a constant b, called the extinction coe▯cient, that satis▯es the equation
▯ = bI:
The dependent variable I represents light intensity, as a function of independent
variable x, representing distance from the light source.
A beacon is lit at night in a ▯eld, measured to have a luminous intensity of 1500
candela as measured at the source (i.e. from a distance of zero). From a distance of
400 m, the intensity is measured to be 220 candela.
a) Determine the value of the extinction coe▯cient b for the air in this ▯eld. 2
b) The average human can no longer detect light from a source when the intensity
of the light drops to 2% of the intensity as measured at the source. If the average
person were to walk away from the beacon, at what distance will they ▯rst be unable
to see the light that the beacon emits? Give your answer to the nearest metre.
3. A simple hot water tank can be modeled by the following ▯rst-order di▯erential
cdT + 1(T(t) ▯ T ) = Q(t);
dt R 0
where the dependen