Recent content by wayneo

This is a question from a test that I have done. I have the answer but am unsure of the working. consider the expansion of (x^2 - 2)^5 a) write the down the number of terms in this expansion b) the first 4 terms of the expansion in descending powers of x are x^10 - 10x^8 + 40x^6 + Ax^4 +...

Im sure I heard my teacher mention using a fibonacci formula and phi etc, any ideas what to come up with?

But the series is an 'infinite fraction' what exactly does that mean?

Im not too sure i follow your L=1+1/L. could you explain it a bit more please

Im not sure if that is the right formula or not : t_{n+1} = 1 + \frac{1}{t_n}

the generalized fomula for tn+1 will have to be : 1 + _1_ tn One of the fibonacci formulas that I think should be used is F_n=((1+sqrt(5))^n-(1-sqrt(5))^n)/(2^nsqrt(5)) but I am not sure how to combine the two to get a generalized formula for tn+1 in terms of tn?

I am stuck how to determine a general formula for tn+1 in terms of tn given that the 'infinite fraction' as a sequence of terms tn is : t1 = 1+1 t2 = 1 + __1__ 1+1 t3 = 1 + ___1___ 1 + __1__ 1+1 It involves the fibonacci sequence.

see I just wanted to be sure whether the book was wrong or not as it says it is 1. I tried working out the determinant step by step and making it equal to 0 then solve for 'k' like an algebra equation

but the answer in the book says +/- 2 how is that

find the values of 'a' for which the equations { ax + y = 7} { 4x + ay = 19} have no solutions. I realize that you have to split it into (a 1) (x) (7) (4 a) (y) = (19) but I am stuck how to find solutions for 'a'...

determine the value of k for which the matrix (2 4 1) (k -1 2) (7 7 4) has no inverse apparently the answer is k = 1 but I can't see how. I worked it out to be -3

D is the distance from the headlights to the lens and b is the diameter of the lens

using theta= 1.22 wavelength / b gives 1.22*(500*10^-9) / 0.05 = 1.22*10^-5 so 1.22*10^-6 = 1.22 wavelength / D so D = 1.22*(500*10^-9) / (1.22*10^-5) = 0.05 the answer i have found in the book is 115km so I am stuck as how to get to that

i have tried that but it doesn't work.

the headlights of a car are separated by a distance of 1.4m. at what distance would these be resolved as 2 separate sources by a lens of diameter 5cm if a wavelength of 500nm is being used ? using theta=1.22 * wavelenth / D I am stuck as I don't know what angle theta is or how to work it out.