Posted by David. on Friday, October 23, 2009 at 12:37am.
Can someone help me step by step how to find the answer to this problem.
The amount of air in a balloon at time t is given by the equation
a(t)=3tsint+t^2 where t is measured in seconds and the amount of air is measured in cubic centimeters.
a. what is the amount of air in the balloon after 10 seconds.
b. is the amount of air in the balloon increasing or decreasing at t=4 seconds and at what rate ?
c. When does the amount of air in the balloon reach 30 cubic centimeters?
THANK YOU!

Calculus AP  MathMate, Friday, October 23, 2009 at 7:40am
a. t=10
Evaluate a(t)=3tsint+t^2 using t=10, i.e.
a(10)=3(10)sin(10)+(10)^2
b.
find a'(t)=da/dt using the product rule and the sum rule. Then evaluate a'(4) to see if it is positive (increasing) or negative (decreasing).
Product rule : d(uv)/dt = udv/dt+vdu/dt
Sum rule : d(p+q)/dt = dp/dt + dq/dt
In the given expression for a(t),
a'(t) = d(3tsint+t^2)
=d(3t.sin(t) )/dt + d(t²)/dt
=3sin(t)+3t.cos(t) + 2t
Evaluate a'(4) to verify the sign.
c. When it reaches 30 cm³,
3tsint+t^2 = 30
Solve for t by trial and error or newton's method. The answer should be around 6.
Answer This Question
Related Questions
 Help me! Geometry  A design on the surface of a balloon is 5 cm wide when the ...
 calculus help me plz too hard show step  charge Q coulombs at time t seconds is...
 Calculus  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 ...
 Calculus  Find the equation of the tangent to the curve y=2e^x at the point ...
 Physics  Hello recently I was asked to find the time it takes a satalite that ...
 Algebra  in that equation I have to solve for x. 5. x^3 + 2x^2  9x = 18 in ...
 Calculus  Use the fourstep process to find the slope of the tangent line to ...
 Calculus  The rate of change R, in kilometers per hour, of the altitude of a ...
 ALGEBRA HELP  When solving the equation, what property was used to go from step...
 Algebra 1StepbyStep  Can someone show me how to solve these stepbystep? ...
More Related Questions