Posted by Craig on Tuesday, November 25, 2008 at 7:54pm.
sorry about that: when t=0, r't=5.7;
t=2, r't=4; t=5, r't=2; t=7, r't=1.2; t=11, r't=.6; t=12, r't=.5
i really don't know how to start this problem
I have not answered your question since I am somewhat puzzled by the wording of your question.
by <<The radius of the balloon in feet is modeled by a twice-differentiable function of r of time t>> do you mean that r is a quadratic function of t, a cubic or what?
As I see it, I could differentiate a function any number of times, just because I might reach a derivative of zero does not mean I couldn't do it once more.
e.g y = x^3 + ...
y' = 3x^2 ....
y'' = 6x ....
y''' = 6
y'''' = 0
y ''''' = 0
i'm guessing that twice differentiable means y''
agree, but what level is the function?
e.g. If I knew that y = ... is quadratic, I could say y = at^2 + bt + c and go from there, but how do I know it's not a cubic?
It does not matter I think.
We are not fitting the entire data set with a function but doing linear, then quadratic, interpolation.
For part a use radius at 5 and dr/dt at 5
r(5.4) = r(5) + .4 r'(5)
r(5.4) = 30 + .4 (2)
r(5.4) = 30 + .8
r(5.4) = 30.8
V = Volume = (4/3) pi r^3 in ft^3
DV/dt = (4/3) pi (3) r^2 dr/dt in ft^3/sec
at t = 5
dV/dt = 4 pi r^2 (2)
= 8 pi (30)^2 = 240 pi ft^3/second
NOTE - the rate of change of volume is the surface area, 4 pi r^2 times the rate of change of radius - think about it.
Related Questions
physics - a hot air balloon rise above the ground, accelerating upwards at a ...
chemistry - hot-air balloon is filled with air at a volume of 3.64 x 10^3 m^3 at...
geometry - Hot air balloons require large amounts of both hot air and fabric ...
Chemistry - A hot air balloon is filled with 1.39 × 106 L of an ideal gas ...
science - You are a maker of hot air balloons and wish to construct a balloon ...
Physics - Hot air balloons float in the air because of the difference in density...
Craig - baloon - calculus moved up - Posted by Craig on Tuesday, November 25, ...
Physics :(( help please TT - You are a maker of hot air balloons and wish to ...
calculus - You are letting the air out of a hot air balloon at a steady rate. ...
physics - On a perfect fall day, you are hovering at low altitude in a hot-air ...
For Further Reading
