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    Distance from a 3 space line

    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...
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    Inverse trig function

    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.
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    Polar to Cartesian conversion - how related?

    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...
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    Inequality question (when fraction < zero)

    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...
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    Linear Algebra / Gaussian Elimination

    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?