Craig  baloon  calculus moved up
posted by Damon .
Posted by Craig on Tuesday, November 25, 2008 at 7:54pm.
t: 0 2 5 7 11 12
r'(t): 5.7 4.0 2.0 1.2 0.6 0.5
The volume of a spherical hot air balloon expands as the air inside the balloon is heated. The radius of the balloon in feet is modeled by a twicedifferentiable function of r of time t, where t is measured in minutes. For 0<t<12, the graph of r is concave down. The table above give selected values of the rate of change, r'(t), of the radius of the balloon over the time interval 0<t<12. The radius of the balloon is 30ft when t=5.
a)est. radius of balloon when t=5.4 using tan line approximated at t=5. Why?
b)Find rate of change of the volume of the balloon w/ respect to time when t=5. what is the units of measure?
Responses
* Calculus  Craig, Tuesday, November 25, 2008 at 7:56pm
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
* please help!!!  Craig, Tuesday, November 25, 2008 at 9:55pm
i really don't know how to start this problem
* Calculus  Reiny, Tuesday, November 25, 2008 at 10:49pm
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 twicedifferentiable 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
* Calculus  Craig, Tuesday, November 25, 2008 at 11:00pm
i'm guessing that twice differentiable means y''
o Calculus  Reiny, Tuesday, November 25, 2008 at 11:33pm
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?
* Calculus  Damon, Wednesday, November 26, 2008 at 6:23am
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
* Calculus  Damon, Wednesday, November 26, 2008 at 6:29am
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.
Respond to this Question
Similar Questions

math..percents
Craig wants to buy some software for his computer. The company that makes the software sells it to a software distributor for $30. The distributor adds 15% to the price and then sells it to the store. The store adds 25% on top of the … 
2nd Grade Math
Craig reads a book with 10 pages in the morning, a book with 26 pages before dinner, and a book with 10 pages after dinner. Find the mode of the number of pages in the books that Craig read. 
physics
Posted by sandhu on Tuesday, November 30, 2010 at 7:38pm. Posted by sandhu on Tuesday, November 30, 2010 at 1:17am. A T is made of two identical 740 g thin solid rods. The moment of inertia of the T about an axis perpendicular to the … 
Math
Craig reads a book with 10 pages in the morning, a book with 26 pages before dinner, and a book with 10 pages after dinner. Find the mode of the number of pages in the books that Craig read. 
math
craig reads a book with 10 pages in the morning a book with 26 pages before dinner and a book with 10 pages after dinner find the mode of the number of pages in the books that craig read 
Finite Math
Laurie and Craig have purchased a new home. They paid $25,000 down and have a 15year mortgage for which they pay $980 per month. If the interest is 8.25% compounded monthly, what did the house that Laurie and Craig purchased originally … 
math
Write an equation to represent each situation: 1)Juanita has 102 beads to make n necklaces. Each necklace will have 17 beads. 2)Craig is c years old. His 12yearold sister Kaitlin is 3 years younger than Craig. 3)Kim rented skates … 
Math
Craig scored 12 points in a game. Marla scored twice as many points as Craig but 5 fewer points than Nelson scored. How many points did Nelson score? 
Math
Craig used the diagram to compute the distance from ferris to dunlap to butte. how much shorter is the distance directly from ferris to butte than the distance craig found? 
Business Math
Craig runs a business importing shoes from Italy and selling them in Namibia. For the below questions (a – g), rounds your answers to cents (two decimal places). a) If the Euro / Namibian dollar exchange rate is € 1 = N$ 13.90 …