Click here to go to the NEW College Discussion Forum

Given:
triangle ABC
angle C = approximately (1/sqrt(atm))/2, where "atm" is one atmosphere (pressure) in megapascals (MPa).
BC = 5 units

Find:
The length, in units, of AB and AC so that AB=AC.

Happy hunting.

By Pat57575 (Pat57575) on Monday, February 03, 2003 - 12:21 am: Edit

kind of a strange problem eh? Angle C is 90 degrees so AB and AC can't equal each other. (AC is a leg while AB is the hypotenuse)

By Quarky (Quarky) on Monday, February 03, 2003 - 12:40 am: Edit

Good job Pat. The main idea of the problem was for people to see an interesting calculation:
1/sqrt(atm) = 3.14153, which is awfully close to Pi. What a coincidence!

So why do you claim that AB and AC can't equal each other? What's your argument? Why can't a leg of a right triangle equal the hypotenuse?

By Pat57575 (Pat57575) on Monday, February 03, 2003 - 12:59 am: Edit

AC^2 + 25 = AB^2
AB^2 + 25 = AB^2
25 = 0 (unsolvable)

however...

AC = (AB^2 - 25)^[1/2]

lim AC as AB approaches infinity = lim (AB^2 - 25)^[1/2]) = infinity

lim AB as AB approaches infinity = infinity

Therefore, when AB equals infinity, AB = AC

sorry, I felt the need to make stuff up.

By Quarky (Quarky) on Monday, February 03, 2003 - 04:59 pm: Edit

No apologies needed! That's exactly that I was looking for! Good thinking.

infinity = crazy.

By Heatwave345 (Heatwave345) on Monday, February 03, 2003 - 09:11 pm: Edit

since we are on the topic of crazy things...

anybody know why e^(i(pi))=-1?
(pi)=3.1415926..., e=2.7182...,i=sqrt(-1)


Also i need help on an AP Calculus BC question. We had this on a test and NOBODY got this question right. We have to do test corrections and i have no clue how to do this question. Here is it:

A tank initially contains 100 gals of pure water. Then at t=0 brine containing 5 lb of salt water per gallon enters the tank at a rate of 10 gal/min and the mixture is allowed to drain from the tank at 5 gal/min. How much salt will the tank have at an arbitrary time t? How much salt will the tank have when it contains 200 gallons of solution?


BTW we have to show work, so the use of the 89 is not allowed.

By sauce on Monday, February 03, 2003 - 09:35 pm: Edit

Are the dimensions of the tank given?

By sauce on Monday, February 03, 2003 - 10:00 pm: Edit

Well, from what I can tell, the salt is entering in at a rate of 25 lb/min? There will be 500 lb. of salt when there is 200 gallons of solution?

I haven't done calculus for quite a while, so I'm still kind of rusty.

By bumper on Tuesday, February 04, 2003 - 03:16 pm: Edit

bump

By hmm on Thursday, February 06, 2003 - 11:16 pm: Edit

let amount of salt in tank be S(lbs)
+5gal/min
dS/dt in = 50lbs/min
dS/dt out = 5(gal/min) / (100(gal)+5(gal)xt) x S(lbs) (gals cancel and you get lbs/min)
= 5S/(100+5t)
dS/dt = 50 - 5S/(100+5t)

i bet there something careless/stupid in there ... but you might be able to solve the diffEQ...

my school wont let anyone skip calc AB.. :'(

By Forhad on Thursday, February 20, 2003 - 03:38 pm: Edit

This is a response to HeatWave... I was also, back in the days, perplexed about the question you have posed here, and I didn't know enough math to understand why the equation is the way it is... But I have learned why it is so. It has to do with the topic of Taylor Series and Complex Analysis.

Eventually, all the analysis leads to a beautiful formula that Euler found which allows one take -e- to any complex power:

e^(u*i) = cos(u) + sin(u)*i

as a special case of this formula, letting u = pi produces -1 on the right hand side of the equation.

The proof for Euler's formula is fairly simple to understand if you know the concept of power series. here is a version of the proof:

http://www.math.toronto.edu/mathnet/questionCorner/epii.html