Homework Statement
How many combinations of people are there if you choose 4 or 5 from a group of 10?
Homework Equations
Relies on binomials
The Attempt at a Solution
binomial (10,4) = binomial (10,6) = 210
But when choosing 5 the answer is binomial (10,5) / 2 = 126
Why do I need to divide by 2?
My thinking started with wind gusts. I was more thinking if one is bed and the neighbor is noisy could a fan be used to deflect the sound waves around one' s head.
I didn't mean the turbulent air would change the speed of sound in the still air, I meant relative to the still air. I don't...
If I turn on a standing fan in my room how does the speed of sound change in the fast moving air compared to the still air around it? Would it be relatively faster, slower, or does it depend on the direction in which the fan is blowing?
Assuming the parabolic walls are long enough won't a parabola give you the same result, but only for rays parallel to the central axis. All rays parallel to the central axis will reflect through the focal point, continue through the focal point and hit the opposite parabola wall, and they will...
Is there a time limit on editing previous posts? Or at least to mark that I've realized I've written something that doesn't make sense
This should be changed to, "all light in front of the parabola that is parallel to the central axis will go through or has originated from the focal point of...
What program did you use to make this? I made my own attempt on paper.
I think the answer I was looking for is, all light parallel to the axis goes through the focus, even if the light source is off axis. Yes it's obvious but it didn't make sense till I drew it.
I can do that when I get home, but then is my ray drawing for the spherical mirror correct, where off axis light sources end up parallel to the central axis?
It's actually a concave spherical mirror, I didn't know how to sketch a parabola, so I thought it was a good enough approximation.
Edit: i see that was a mistake
If I trace the ray back and out through the focus then the angle of incidence and reflection aren't equal. Which must mean there is something very wrong with my parabola sketch, but I can't see it.
I used the focal point to determine the normal at each of the points where my source ray reflected of the parabola wall.
And the results are, as can be seen in my rough and ready image in yellow, if it hits the parabola walls twice it ends up parallel to the central axis. I almost didn't believe...
Yeah sorry I should have been more clear.
The incoming ray reflects of the parabola wall through the focal point then reflects of the parabola wall on the opposite side of the focal point back to the light source.
In this case what happens to rays shining into the parabola not parallel to the...