## #math - Thu 10 May 2007 between 02:07 and 02:05

### NY Lost Funds

 mk_ but how do I figure out the distance? TRWBW mk_: c(t)=c0+t*v, define the line with a unit normal to it, get a quadradic mk_ since there are an infinite number of points on the lineunit normal to it? TRWBW mk_: define the line as ax+by=c, or {a,b}.{x,y}=c mk_ alright TRWBW mk_: {a,b} is a normal vector to the line anubiss i have some problems with trig identities:i have to integrate sqrt(1 -sin(t) ) TRWBW mk_: if it's a unit normal, then |{a,b}.{x,y}-c| is distance to the line Eclipsor substitute, anubiss ? mk_ what is the {a,b}.{x,y} notation? Eclipsor and remember that cos is an evil derivative because it turns sin negative while sin is all peaceful and turns into positive cosine :) anubiss i can use the conjugate to obtain: sqrt( 1 - sin(t) ) * ( ( 1+sin(t) ) / ( ( 1+ sin(t) ) ) TRWBW mk_: i use . for dotmk_: raise it up half a line height and it looks like dot product mk_ ...multiplication? anubiss and the answer book gives after this step : sqrt( cos^2(t) / sqrt(1+ sin(t)and i dont undetstand droptothetop In relation to existence and uniqueness of a solution to a differential equation, if it's determined that there is no unique solution given a certain initial condition how can you show that there is more than one solution?One way would be to solve the equation. anubiss first i dont understand how you can multiply 1 - sin(t) by 1+ sin(t) and second the answer cos^2 .. droptothetop But how to show that there are two? TRWBW droptothetop: how about f+1=f, that's a differential equation with no unique solution Olathe anubiss: (1 - sin)(1 + sin) = 1 - sin^2. cos^2 + sin^2 = 1. anubiss okfirst i dont understand how you can multiply sqrt(1 - sin(t)) by sqrt(1+ sin(t)).. they are different! Olathe anubiss: (1 - sin)(1 + sin)/(1 + sin) droptothetop TRWBW, well, I am speaking specifically about ones that are given initial conditions, and at those initial conditions there is discontinuity in f(y,t) in y'=f(y,t) anubiss hum, well my problem boils down to the sqrt's Olathe anubiss: a = ab/b anubiss why do you remove them TRWBW droptothetop: f=1+f, f(0)=1 droptothetop or in d f(y,t) /dy Olathe anubiss: Where are they removed ? mk_ ok, I see what the dot product is. I use a and b from the line, and x and y from the circle... what's c then? anubiss i see so you dont care about the sqrt's you just multiply whats insidekk TRWBW mk_: that lets you shift the line.