maths problem (1 Viewer)

[professor]

mm...got this question for hw and i am really stuck on it...hope u einsteins out there can enlighten my day up

Given 2 straight lines y=m1x and y=m2x, show that the bisector of the angle between these lines is the line y=mx where
(m-m1)(1+mm2) = (m2-m)(1+mm1)
Note: keep the m'm in cyclic order i.e. use m-m1 and m2-m
thus showing that the gradients of the 2 bisectors is given by the quadratic in m (m1+m2)m^2 +2(1-m1m2)m -(m1+m2) =0

and write down the product of the roots. What relationship is indicated between the 2 bisectors...

 

[spice girl]

Let m1 = tanP, m2 = tanQ
so m = tan((P+Q)/2) for it to be bisector

so tan(P - (P+Q)/2) = tan((P+Q)/2 - Q)

use compound angles for tan function:

(m1-m) / (1+mm1) = (m-m2) / (1+mm2)

Cross multiply to get 1st question

Expand and regroup to get required quadratic in m

remember that product of roots of am^2 + bm + c is c/a

this happens to be -1

thus significance: two bisectors are perpendicular

 

[Saintly Devil]

another question - in regards to probability (i know, it's a 2u topic, but we got it in our 3u test)

In a town, the likelihood of voting Labour is 55%, Liberal 40% and Greens 5%.
In a house live 3 people. What is the probability that each of them will vote for a different party?

I'm not totally sure how to do this question. Is it the simple matter of doing 0.55*0.4*0.05 ?

 

[ND]

Originally posted by Saintly Devil
another question - in regards to probability (i know, it's a 2u topic, but we got it in our 3u test)

In a town, the likelihood of voting Labour is 55%, Liberal 40% and Greens 5%.
In a house live 3 people. What is the probability that each of them will vote for a different party?

I'm not totally sure how to do this question. Is it the simple matter of doing 0.55*0.4*0.05 ?

Now i haven't done probability of any kind (neither 2u, 3u, nor 4u), but from common logic, it would seem that there are 6 ways for this to occur, so i think it would be 6*0.55*0.4*0.05

 

[BlackJack]

Originally posted by Saintly Devil
[B}
I'm not totally sure how to do this question. Is it the simple matter of doing 0.55*0.4*0.05 ? [/B]

...
yeah, seems it's 6* times...