How do you solve this problem?
An artery has a circular cross section of radius 4 millimeters. The speed at which blood flows along the artery fluctuates as the heart beats. The speed after t seconds is 50+9sin(2pit) meters per second.
What volume of blood passes along the artery in one second?
V = _____cubic millimeters
The distance s which the blood flows in time t is:
s = int[ v ] dt
where v is the speed given.
As the result is required in mm^3, and the speed is given in m/sec, you multiply by 10^3 to convert the given speed to mm / sec.
As you want the volume flowing from t = 0 to t = 1, 0 and 1 are the lower and upper limits respectively of the integral.
The cross sectional area of the artery is:
pi 4^2 mm^3.
You then multiply the distance the blood has flowed by the cross-sectional area to get the volume in 1 sec.
Hence:
V = (pi 4^2) 10^3 int(0, 1)[ 50 + 9 sin(2pi t) ] dt
= (1.6pi * 10^4) [ 50t - 9 cos(2pi t) / (2pi) ](0, 1) mm^3
As cos(2pi) = cos(0):
V = (1.6pi * 10^4) * 50 mm^3
= 2.51 * 10^6 mm^3.
Heart Beat in after effect
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Digital Automatic Auto Wrist Blood Pressure Pulse Monitor Heart Beat Meter $13.79 |
|
|
Digital Wrist Blood Pressure Monitor & Heart Beat Meter $15.99 |
|
|
Digital Wrist Blood Pressure Monitor & Heart Beat Meter (With 3X33 Memories) $2.00 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Auto Digital Upper Arm Type Blood Pressure Meter & Heart Beat Monitor 99 Data $27.90 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Digital wrist blood pressure monitor/heart beat meter $16.59 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Digital Automatic Wrist Blood Pressure Pulse Monitor Heart Beat Meter $15.49 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |
|
|
Newest 60 Meomories Digital Wrist Blood Pressure Monitor & Heart Beat Meter BPM1 $0.99 |