24. (a)
Note that the level of the coffee in the cone is not
needed until part (b).
Step 1:
V
1
5
volume of coffee in pot
y
5
depth of coffee in pot
Step 2:
}
d
d
V
t
1
} 5
10 in
3
/min
Step 3:
We want to find the value of
}
d
d
y
t
}
.
Step 4:
V
1
5
9
p
y
Step 5:
}
d
d
V
t
1
} 5
9
p
}
d
d
y
t
}
Step 6:
10
5
9
p
}
d
d
y
t
}
}
d
d
y
t
} 5 }
9
1
p
0
}
<
0.354 in./min
The level in the pot is increasing at the rate of
approximately 0.354 in./min.
(b)
Step 1:
V
2
5
volume of coffee in filter
r
5
radius of surface of coffee in filter
h
5
depth of coffee in filter
Step 2:
At the instant in question,
}
d
d
V
t
2
}52
10 in
3
/min and
h
5
5 in.
Step 3:
We want to find
2}
d
d
h
t
}
.
Step 4:
Note that
}
h
r
}
5 }
3
6
}
, so
r
5 }
h
2
}
.
Then
V
2
5 }
1
3
}
p
r
2
h
5 }
p
1
h
2
3
}
.
Step 5:
}
d
d
V
t
2
} 5 }
p
4
h
2
} }
d
d
h
t
}
Step 6:
2
10
5 }
p
(
4
5)
2
} }
d
d
h
t
}
}
d
d
h
t
}52}
5
8
p
}
in./min
Note that
}
d
d
h
t
} ,
0, so the rate at which the level is
falling
is positive. The level in the cone is falling at the
rate of
}
5
8
p
}
<
0.509 in./min.
25.
Step 1:
Q
5
rate of CO
2
exhalation (mL/min)
D
5
difference between CO
2
concentration in blood
pumped to the lungs and CO
2
concentration in blood
returning from the lungs (mL/L)
y
5
cardiac output
Step 2:
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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