Recent content by Michael_Light

Got it. Your hint is very useful. Thanks.

Homework Statement Suppose there is 7 chairs arranged in a straight line, each of the 3 boys will sit randomly on one of the chair . In how many ways the boys can be seated if the 3 boys cannot sit next to each other? Assume that the boys are indistinguishable. I listed out all the...

Homework Statement Homework Equations The Attempt at a Solution I understand that matrix in the form of A as above represents a rotation about the origin.. but for this question, I am actually clueless on what method should i use to prove it... Any hint?

Hi... I read this from my lecture note, but i couldn't understand: i) the red part, shouldn't it be k =0 instead of k=1? ii) the third line to the fourth line... i.e. I have no idea how to change from the third line to the fourth line.. Can anyone enlighten me? Thanks a lot.. :smile:

Homework Statement When cos(4θ)=cos(3θ). prove that θ=0, 2∏/7, 4∏/7, 6∏/7 Hence prove that cos(2∏/7), cos(4∏/7), cos(6∏/7) are the roots of 8x3+4x2-4x-1 Homework Equations The Attempt at a Solution I can do the first part, but i have some difficulty in solving the second...

Sorry.. i mean root.. not factor.. so is this statement correct then? If a cubic equation, f(x) has a root of (3+√2), then the conjugate of the root, (3-√2) is also a root for f(x).

Homework Statement If a cubic equation, f(x) has a factor of (3+√2), then the conjugate of the factor, (3-√2) is also a factor for f(x). Homework Equations The Attempt at a Solution Just to confirm is that statement correct? I read it else where but i not sure is it correct or...

Thanks.. but i still don't understand.. I know that number of e- received by chlorine = number of e- released by S2O32- but the problem is how i find the number of e- released by S2O32- from the information given? Please guide me..:confused:

Homework Statement One mole of aqueous S2O32- ions reduces four moles of Cl2 molecules. What is the oxidation state of the sulphur containing product of this reaction? Homework Equations The Attempt at a Solution oxidation state in S2O32- = +2 since 4moles of Cl2 are reduced...

Homework Statement i) Is lactic acid,CH3CH(OH)COOH a stronger or weaker acid than propanoic acid (CH3CH2COOH) ii) Another question is does ketone reacts with phosphorus pentachloride PCl5? Homework Equations The Attempt at a Solution (i) I guess lactic acid is a stronger acid...

I still have doubts, but this is how i interpret what you guys wrote... Assuming the '2' is distinguishable, then it will have 63 =120 arrangement. If only one card with digit '2' two is taken, it will be 5P3 =60 arrangement. If both cards with digit '2' are taken, it will be 4 x...

Homework Statement I have 6 cards with the digits 1,2,2,3,4 and 5 written on each of them. In how many ways can I arrange 3 out of the 6 cards in a row? Homework Equations The Attempt at a Solution Case 1: Only one card with digit '2' two is taken, so 5P3 =60 Case 2: Both cards with digit...

Homework Statement By expressing xx as a power of e and using the exponential series, or otherwise, find (without using tables) the value of xx when x=0.01, correct to three places of decimals. (ln10 = 2.30 to two decimal places). Homework Equations The Attempt at a Solution I...

Homework Statement Find all the terms up to and including x2 in the power series for tan(ex). Homework Equations The Attempt at a Solution I wonder can i expand it as follow... why will i get different answer when I use Maclaurin's Series to expand it?