The rate of increase of thickness of ice on a pond is inversely proportional to the thickness of the ice is x centimetres and the temperature of the air above the ice is -a degrees celcius, the rate is (ax/14400) cm/s. Form an appropriate differential equation, and hence show that, if the -10 degrees celcuis, the time taken for the thickness to increase from 5 cm to 6 cm is a little more than 2 hours.
2007-08-13 09:40:42 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Asking the same question twice?
Go do your own homework.
Try solving it and then asking if the answer is correct.
JBV^_^
2007-08-13 09:47:01 · answer #1 · answered by jackbassv 3 · 2⤊ 0⤋
This is a rate of change question. The way i was taught to approach this is to have a "find, when, given". For the find have a rate of the form (dy/dt) where a certain component of the question is changing over time and you are trying to find it. The when is at a certain time, and this is of the form t= or x= but it will be in the question. The given is any information remaining in the question. Now form an equation that you already know with all of these components. For example if you were dealing with a circle whose circumference was changing in size you would use the equation C=2pir. I hope this information helps. Seeing as you don't have to solve the full question but just get a differential equation that should not be a problem. Good luck
2007-08-13 09:48:18 · answer #2 · answered by V 2 · 0⤊ 0⤋
First, therapy for y ': y ' (x²y) = a million - x² + y² - x²y² = (a million - x²) + y²(a million - x²) = (a million - x²)(a million + y²) y ' = (a million - x²)(a million + y²) / (x²y) = [(a million - x²)/x²] [(a million + y²)/y] So it extremely is separable! [y /(a million + y²)] dy = [x²/(a million - x²)] dx Edit: in certainty mentioned that I inadvertently inverted the term multiplying dx, making it better good than it extremely is. Im useful you could verify it out. For the y-integration, enable u = a million + y². Edit: you could forget approximately this section. For the x-integration, observe that x²/(a million - x²)] = (x² - a million + a million)/(a million - x²) = -a million + a million/(a million - x²) Use partial fractions to confirm that a million/(a million - x²) = ½(a million/(a million-x) + a million/(a million+x)) you could end.
2016-11-12 05:43:59 · answer #3 · answered by ? 4 · 0⤊ 0⤋
Rate of increse of thickness of ice: x ( cm/s)
Thicness of ice: y
Temperature in air: t
Given information: x = k/yt = k/t y
x = F(y) = k/t f(y) = k/t d/dy (1/y)
= k/t 1/y^2
Put in your given numbers and find the kostant factors.
2007-08-13 10:26:32 · answer #4 · answered by anordtug 6 · 0⤊ 0⤋
Isn't this your homework?
Try supplying the equation.
2007-08-13 09:47:02 · answer #5 · answered by Rocket Scientist X 2 · 2⤊ 0⤋