The sides of this rectangle increase in such a way that dz/dt=1 and dx/dt=3dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt?
First we create a relationship in about this problem. and we got this z^2=x^2+y^2
then we find the derivative of that relationship.
2z dz/dt=2x dx/dt + 2y dy/dt. The two are reduces z dz/dt= x dx/dt + y dy/dt.
By the pythagorean theorem we found that z=5. So after that we just plug in the values.
(5)(1)=4(3)dy/dt+ 3 dy/dt
=15 dy/dt / 5
= 1/3 dy/dt
Since dx/dt= 3 dy/dt we got the value of dx/dt= 1.
Now our pre-test was done all we have to do is study for our test on Tuesday. Good Luck guys.... The next scribe is Steve....