finding asymptotes / acceleration, velocity, position fcns /

[DaAzNJRiCh]

You don't need to answer all the questions one is enough. I need this by tomorrow morning if possible.

1) How do I find all the asymptotes (oblique, vertical, horizontal) of this function?
(3x-2)/(square root of (2x^2 + 1))? Am I supposed to rationalize the denominator because I can't seem to do it.

2) Also this is kinda hard to explain but I need to find the point marked on this picture that uses the shortest combined length of lines. Disregard the faint stuff in the background. The measurements are 5 ft, 12 ft, and 3 ft.
http://s3.photobucket.com/albums/y98/Da ... h=imgAnch1
The second part of the question is that if the line on the left costs double the price of the line of the right then where should the point be?

3) Final question is a plane is going to take off. It is taxiing along at 1 ft/s before it speeds up at a constant acceleration. If it takes 900 ft to take off and takes off at a velocity of 93 ft/s, then what is the acceleration function, velocity function, and position function?


THanks.

 

[skeeter]

How do I find all the asymptotes (oblique, vertical, horizontal) of this function?
(3x-2)/(square root of (2x^2 + 1))? Am I supposed to rationalize the denominator because I can't seem to do it.

for this particular rational function ...

degree of the numerator < degree of the denominator ...
horizontal asymptote at y = 0

the denominator can never equal 0 ... no vertical asymptote.

you will only get an oblique linear asymptote if the degree of the numerator is 1 greater than the degree of the denominator. not the case here.


hint for the 2nd problem (if what you show as right angles are right angles) ...

bottom length = \(\displaystyle \sqrt{140}\).

name one length from the "dot" to the corner x, the other length will be
\(\displaystyle \sqrt{140} - x\).


last problem ...

\(\displaystyle \L a = \frac{(v_f)^2 - (v_i)^2}{2d}\)

once you figure acceleration ...

\(\displaystyle \L v = v_i + at\)

\(\displaystyle \L x = x_i + v_i t + \frac{1}{2}at^2\)