question 1 ) Water leaks from a vertical cylindrical tank through a small hole i

Question

question 1 )

Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 250 liters and 20 liters leak out during the first day.

A. When will the tank be half empty?

t= days?

How much water will remain in the tank after 4 days?

volume =    Liters?   

A thermometer is taken from a room where the temperature is 24 C to the outdoors, where the temperature is 8C. After one minute the thermometer reads 8 C.
(a) What will the reading on the thermometer be after 2 more minutes?

(b) When will the thermometer read 7 C?

part be answer is minutes after it was taken to the outdoors.

*C is dgree in celsius

Explanation / Answer

1)dv/dt =k v1/2

v-1/2dv=kdt

integrate

v1/2=kt+c

v=(kt+c)^2

v(0)=250

250=(0+c)^2==>c=sqrt250=15.81

v(1)=250-20

230=(k+c)^2==>k=sqrt230 -sqrt250=-0.6456

v(t)=250/2=125

125=(kt+c)^2

==>t=7.17=7.2days

after 4 days

v(4)=(4k+c)^2=174.96=175litres

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