A ruptured oil tanker causes a circular oil slick on the surface of the ocean. P

Question

A ruptured oil tanker causes a circular oil slick on the surface of the ocean. Pay close attention to the units in this problem. When the radius of the oil slick is 140 meters, the radius is expanding by 0.2 meter/minute. At that moment, how fast is the area of the slick expanding? Convert your answer to square meters per second. Exact: m^2/sec Rounded to 2 decimal places: m^2/sec Suppose we also know that the thickness of the oil slick remains uniform and the volume of oil spilled remains fixed. At the time referred to in part (a), the thickness of the oil slick is 0.02 meters. How fast is the thickness of the oil slick decreasing? Convert your answer to millimeters per second. (Recall: 1 m = 1000 mm) Exact: mm/sec The circulation time of a mammal (the average time it takes for all the blood in the body to circulate once and return to the heart) is proportional to the fourth squareroot of the body mass of the mammal. Circulation time, T, is measured in seconds and body mass, m, is measured in kilograms. If the proportionality constant is 17.3, write a formula for the circulation time of a mammal. Use a lower case m. T(m) =. The body mass of a growing child is 35 kg and is increasing at a rate of 0.1 kg/month. What is the rate of change of the circulation time of the child? Round your answer to 3 decimal places. sec/month

Explanation / Answer

1.a) A = piR^2

dA/dt = 2piRdR/dt
dA/dt = 2pi*140*0.2
dA/dt = 56 pi m/min

b)
V = piR^2h

= pi(140^2)(0.02)

= 392pi m^3

V = piR^2h

h = V/(piR^2)

= (V/pi)R^-2

dh/dt = -2((V/pi()R^(-3))(dR/dt))
dh/dt = -2(392)(140^-3)(0.02)
dh/dt = -5.714286E-6 m/min

2. a) T(m) =17.3(m)^(1/4)

b)dT/dt =(17.3/4)m^(-3/4)dm/dt

dT/dt = (17.3/4)(35)^(-3/4)(0.1)

=0.0300sec /month

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