hamzah

At time t hours, the rate of decay of the mass of a radioactive substance is proportional to the mass x kg at that time. (a) Write down the differential equation satisfied by x. (b) Given that x = C when t = 0, show that x = Ce^[-(at)], where a is a positive constant. I can't figure out part (a)...so I cant do part (b). So if somebody could help me with part (a) please. thanks

I received a newsletter from Mresenne a few months ago that stated: On November 17th GIMPS member Michael Shafer at Michigan State University proved 2^20996011-1 prime. At over 6.3 million digits it is easily the largest known prime number, beating GIMPS' 2 year old record of just over 4 million digits.

Yeah I do understand what is meant by it, but I'm unsure how to, sometimes, proof something by contradiction, such as the above problem (I posted).

I basically want to know the general method of 'proof by condraction' and an explanation behind it, an example I've been given is: Complete the following proof by contradiction to show that (5)^(1/2) is irrational. Assuming that (5)^(1/2) is rational, let (5)^(1/2) = a/b where a and b are integers that have no common factors Then 5b^2 = a^2 -> 5 is the factor of a^2

Well I've completed an experiment to determine the specific heat capacity of Aluminium...and the book quotes "910J/kg.k"...so I thought I'd stick to the same format as them.

thanks Glider and the rest of you for your help

yeah thats what I'm doing, error measurements...but the way I calculated it...does that technique have a name or anything?

Lets say I have three values - 917, 914 and 913. Take an average I get 915 (approx). Now see how far each value is from the average... 917 - 915 = 2 915 - 914 = 1 915 - 913 = 2 (2+1+2)/3 = 2 (approx) so the value is (915 +/- 2) what is this method called?

thanks everyone

I not sure what you mean by bonds, but with annual compound interest...to calculate how much you will have after a given number of years it is: (original value) * (increase)^(number of years) 15% increase would be 115/100 = 1.15 an example would be: £1000 in the bank...with a annual compound interest of 10%...how much is in the bank account after 3 years? 1000 * 1.1^3 = £1331 And in reply to your problem: it would be: (initial value) * (decrease)^(number of hours) 8000 * (0.87)^5

I did try sin[10^40 - int((10^40)/(2pi))]...but none of the calculators I own are accurate enough.

how would I go about finding sin(10^40) ? [10^40 in radians]

The notes in my study guide say: In the rate law the order of reaction with respect to a reactant indicates how many molecules of that reactant participate in the rate-determining step. If a reactant is first order, one molecule reacts in the rds. If a reactant is second order, two molecules react in the rds. example: H2 (g) + 2ICl (g) --> I2 (g) + 2HCl (g) rate = [H2][iCl] The stoichiometric equation tells us that overall, 1 molecule of H2, reacts with 2 molescules of ICl to give the products. But it does not tell us about the individual steps which make up the overall reaction. There is no link between the stoichiometric equation and the reaction mechanism or the rate equation. The rate equation tells us that the rate-determining step involves 1 molecule of H2 and and 1 molecule of ICl, because it is a first order with respect to both.

I understand that the rate-determining step (rds) is the slowest step in a reaction. However I don't really understand how we establish which "step" it is. Here's the problem: Bromine can be formed by the oxidation of hydrogen bromide with oxygen. The following mechanism has been suggested for this multi-step reaction. 1. HBr + O2 --> HBrO2 2. HBrO2 + HBr --> 2HBrO 3. HBrO + HBr --> Br2 + H2O 4. HBrO + HBr --> Br2 + H2O (a repeat of step 3) rate = k[HBr][O2] Explain which of the four steps is the rate-determining step for this reaction. Also I would like to know in general how you establish the RDS for any given reaction provided you're given the rate equation for the reaction. Thanks