Solve the problem.The volume V (in cubic inches) of a cylindrical pipe with length 12 inches is given by V(r) = 12?r2, where r is the radius of the piston (in inches). If the radius is increasing with time t (in minutes) according to the formula r(t) = 
t2, t ? 0, find the volume V of the pipe as a function of the time t.
What will be an ideal response?
V(t) = 
?t4
Mathematics
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Find the general equation of the orthogonal trajectories of the curves for the given equations.The exponential curves y = ce-4x
A. 8y2 = x2 + c B. 4y2 = x + c C. 4y2 = 2x - c D. 4y2 = x2 - c
Mathematics
Evaluate the function.Find f(k) when f(x) = 3x2 + 4x + 5
A. 3k2 + 16k + 5 B. 3k2 + 4k + 25 C. 3k2 + 4k + 5 D. 9k2 + 16k + 25
Mathematics
Solve for the specified variable.I = 
for r
A. r = 
B. r = 
C. r = 
D. r = 
- IR
Mathematics
The following is a polygonal path obtained from Euler's method with n = 4 to approximate a solution f(t) of a differential equation. Indicate whether the following statements are true or false: 
f' 
? 
A. True B. False
Mathematics