Math Is Fun Forum

It looks right to me!
And, it is definitely a minimum...the value of the derivative function around x=2000 confirms it...plus the second derivative [ 1600/(x^3) ]at x=2000 is positive...

It sounds like there were a lot of people from the UK...
I'm a Chicagoan

LOL..
It is way to early for me to be laughing that hard...
I am going to learn how to say cotton in every language...that is a great idea...
also, that joke is absolutely freakin hilarious...right up my alley

I think you had a diet soda...there is something about the sugar in the regular sodas that would keep it from freezing as fast.  (maybe the other way around, but I think I'm right)

I'm having trouble visualizing what you mean...we are talking about a concave quadrangle, right?...Then P is outside of the qdrngle?
I'll keep at it and get back to you, but any sort of clarification so that I could make a picture in my head would help.
Else, if you have since solved this, I would love to see your proof.

1)  I am not certain I am understanding this problem correctly, but here goes...
The graph of the equation x^2+y^2=4 is a circled centered at the origin, of radius 2.
A line drawn from the point (12,0) that is tangent to the circle would intersect the circle at one of the y intercepts.
By drawing this line, we create a right triangle, with a base of length 12 on the x-axis, and a height of 2 on the y-axis.
You can now plug these into the pythgorean formula, yielding the square root of 148

2)  If we let x be the number of pencils Bob had to start with...
the number of pencils he had AFTER he gave some to Barbara is given:   x-(4/5)x   or equivalently, (1/5)x...
then, after he gives some pencils to bonnie, he has:
            (1/5)x-(2/3)(1/5)x    or   (1/15)x

Now this last term is the number of pencils left after he has seen both Barbara and Bonnie, and we know from the problem that this number is ten...hence
      (1/15)x=10    and     x=150  (the # of pencils he had to start)

3)  sorry...I don't know what hamburger style means