Recent content by page13

Homework Statement Find the distance between the line x=3t-1, y=2-t, z=t and the point (2,0,-5) Homework Equations The Attempt at a Solution So I'm assuming I need to use the formula D=[ax+by+cz+d]/root(a^2+b^2+c^2) and I'm guessing I need to use (3,-1,1), extracted from the...

Ah, OK! 24/25 correct?

Homework Statement Find the exact value of the expression: Homework Equations sin[2arcsin(3/5)] The Attempt at a Solution I know you're supposed to use sin2x=2sinxcosx somehow but not sure how to start.

Excellent! That helps a lot. But the last bit about using (x,1) - not sure how you're getting csc=r/x. Wouldn't it still be r/1?

Homework Statement Find the cartesian equation for the curve r=csctheta The Attempt at a Solution I understand how to get the answer, by changing it to r=1/sin, and then rsin=1, and then since y=rsin, then y=1. What I'm not understanding is the relationship between y=1 an r=csc. I...

Awesome. Thanks. Now I can sketch this parametric.

Ah OK. So it's more by inspection. I would factor as we have done, and then I'd choose for example -2, 0 and 2 and determine the sign giving me the interval values around 1 and -1, correct?

So 9(t-1)(t+1), but what do I deduce from that?

Homework Statement Solve for t: [-2(t2+1) / 9(t2-1)] < 0 The Attempt at a Solution I know that the answer is -inf<t<-1 and 1<t<inf, but how do I show the calculation to get that answer? When I tried, I narrowed it down to t<root-1, but that's not possible (without complex...

Thanks Dick. I guess I'll get some big ugly fractions in my Row Echelon Form, correct? So far I've got numbers over 53 in the 1st row, over 65 in the 2nd row, and the 3rd row looks like it'll be a 4 digit denominator.

Homework Statement Find coefficients a,b,c and d so that the curve of a circle in an xy plane, with points (-4,5), (-2,7) and (4,-3), is given by the equation ax2 + ay2 + bx + cy + d = 0. Not even sure where to start. Can anyone help me with this?

Not sure where the quote comes from, but I was just thinking about this the other day. Specifically about how, with the cosmological principle, we must assume that all areas of the universe are typical. This, then, seems to presuppose that the universe that we experience or perceive even...