The vertices of a hyperbola are the two points closest to each other. For hyperbola that is centered at the origin (0,0) the vertices are (a,0) and (-a,0) a) What is 'a' for this hyperbola?

b) The slope for the asymptotes for a horizontal hyperbola are equal to b/a and -b/a.
Use the graph to calculate the slope (as a fraction) for the asymptote with a positive slope. (Use rise/run).

c) Use the slope of the asymptote to find the 'b' value.

d) What is the equation for this hyperbola?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

On a piece of paper graph f(x)=5•(0.4)^x

What is the result of converting 60 ounces to pounds remember there are 16 ounces in a pound