Sorry, I will not be able to answer all of my semi-promised exercises. The UPCAT sked is so toxic, I am writing this midnight and I have to be at UP at 530 am! suicide, huh. haha
Anyway, I’ll just work on some examples of my own and just read between the lines why.
An inlet pipe can fill the pool in 3 hours while a drain pipe will drain the pool in 8 hours. If the inlet pipe is turned on and the outlet pipe is accidentally also turned on after one hour that the inlet pipe gushing, how many more minutes would it take for the pool to be filled halfway?
Soln: rate of inlet pipe is 1/3
rate of outlet pipe is -1/8
Since the inlet pipe has been gushing for 1 hour, it would have done 1 times 1/3 or 1/3 of the work. The equation would look like this:
1 (1/3) + (1/3 + -1/ 8 ) t = 1/2
where t is the time wherein the pool becomes halfway full. You know of course how to solve for this.
Find the value of s such that the perimeter of the the equilateral triangle with side s is equal to the area of the same equilateral triangle with side equal to s.
Soln: We know that the perimeter of an equilateral triangle with side equal to s is 3s and you may verify that the area of the triangle with side equal to s is sqrt(3) s^2 divided by 4. Equate the two and you would get the correct answer.
Posted by ldvallejo 
be the line represented by the symmetric equations
.
and 
Posted by ldvallejo 
be a finite vector space over the set of rationals, and 
be a linear transformation from 
and 
are vectors in 
is nonzero. Show that 
Posted by ldvallejo 
enclosed by the curves 
and 
. Set-up the integrals representing the following:
.
and 
using the method of washers.
using the method of cylindrical shells.
so that its abscissa is increasing at a rate of 
units per second. At what rate is the particle moving away from the origin as it passes through the point 
?
, the line 
and the positive ![\displaystyle y=\tanh \left[\sin^{-1} \left( x-\sqrt{2}\right) \right]](http://l.wordpress.com/latex.php?latex=%5Cdisplaystyle+y%3D%5Ctanh+%5Cleft%5B%5Csin%5E%7B-1%7D+%5Cleft%28+x-%5Csqrt%7B2%7D%5Cright%29+%5Cright%5D&bg=ffffff&fg=333333&s=0 "\displaystyle y=\tanh \left[\sin^{-1} \left( x-\sqrt{2}\right) \right]")
at the point where 
.
.![y=\displaystyle \sqrt[5]{\frac{4^{x}\coth\left(e^{-x}\right)}{\sin\left(x^{2}\ln x\right)}}](http://l.wordpress.com/latex.php?latex=y%3D%5Cdisplaystyle+%5Csqrt%5B5%5D%7B%5Cfrac%7B4%5E%7Bx%7D%5Ccoth%5Cleft%28e%5E%7B-x%7D%5Cright%29%7D%7B%5Csin%5Cleft%28x%5E%7B2%7D%5Cln+x%5Cright%29%7D%7D&bg=ffffff&fg=333333&s=0 "y=\displaystyle \sqrt[5]{\frac{4^{x}\coth\left(e^{-x}\right)}{\sin\left(x^{2}\ln x\right)}}")
