Recent content by DJ24

Is there enough given information to find a numerical value for OB?

Homework Statement A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be...

I see how the discriminant arises by completing the square: (2ax+by)^{2}=(b^{2}-4ac)y^{2} But how does it relate to a parabola when b^{2}-4ac=0?

Is the eigenvalue/vector explanation the only one, though? Isn't there a simple algebraic rearrangement of the general quadratic equation that results in displaying the discriminant?-such as in the quadratic formula of which only involves the variable x?

I am looking for more of an algebraic proof.

I narrowed down my previous question and reposted it because I felt like the last one died. Also, my previous question was not a request of an explanation of the determinant's derivation, but rather the connection between it and conic classification. I feel like there may be a simple proof...

I know where the discriminant comes from in the quadratic formula of which involves only x, but I don't see how it comes from the irreducible general quadratic equation of which involves x and y.

I still do not see the connection between b^{2}-4ac and the classification of a conic.

I understand how the discriminant, b^{2}-4ac, comes from in the quadratic equation ax^{2}+bx+c=0, but how does it come from the general quadratic equation ax^{2}+bxy+cy^{2}+dx+ey+f=0 ?

Oh. I suppose I should have put "as n approaches infinity", given the relationships between n and m, and n and (change in x). I am just trying to intuitively understand how the inverse of the derivative differences (definite integral) of a function is equal to the area bounded by the limits of...

Can someone give me an explanation or possibly a proof that \int^{a}_{b}f(x)dx= \displaystyle\lim_{m\to\infty}\sum^{m}_{k=1}f(x^{*}_{k})\Delta x

Apparently, the definition of area is too sophisticated to be given in any standard calculus textbook. I am unaware of most advanced mathematical notation and would like to know what the U-symbol means. Also, is a two-dimensional set a set of ordered pairs (x,y) where X may be a region? What...

Thanks

The one that is used most often.

How do I insert (more advanced) mathematical notation in a simple thread post?