1. is a constant
sub in the given values and solve for
2.
take the time derivative of the above equation, sub in the given value for and solve for
when , ... also remember that
1. Water flows into a vertical cylindrical tank at the rate of 12 cu.ft/min. The surface rises 6 inches per minute. Find the radius of the tank.
2. If the angle of elevation of the sun is 45degrees and is decreasing at 0.25rad/hour, how fast is the shadow cast on level ground changing(lengthening) when the pole is 50ft tall?
My Effort..
1.
Sol'n:
V=Bh
V=pi (r^2) h --> is used this as my working equation
dV/dt = 2pir(dr/dt)(dh/dt)
..i stopped in here because it noticed that there is no rate for radius, so what I did is to work again..
V=Bh
V=pi (r^2)h
r= sqrt.(V/pi h) --> this is my another working equation
r = sqrt[ (dV/dt)/ pi (dh/dt) ]
r = 2.76 ft
There it goes.. I don't know if it is correct.
2.
Sol'n:
tan 45 = 50/x
x = 50/tan45 --> this serves as my working equation
dx/dt = [-50sec^2 (45) (0.25rad/hr)] / tan^2 (45)
dx/dt = -25ft/hr
There is all my effort. Tell me all the corrections.
Thanks!
hmmm...
sir, i tried both equations inverse and not inverse, it just came up with the same answer..
this is how i made them both..try to see if there is a mistake,
the second column is to how I understand your explanation awhile ago.
Yeah! I remember now..since the elevation of the sun is decreasing the angle should be negative..am i right?
Thanks a lot for the help! ^_^ I really appreciate the whole thing.
By the way, it is our examination week this week, as for our first schedule today, calculus, can you give me some tips? The coverage of the exam are differentiation, related rates, tangent line and normal line and applications of derivatives of trigonometric and inverse trigonometric function.
Thanks a lot!