Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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The number of liters of blood your heart pumps in a minute is called your cardiac output.To measure a patient’s cardiac output doctors may use the dye-dilution technique (inject 5-10 mg of dye in a main vein near the heart and measure its concentration). To calculate the patient’s cardiac output, we divide the amount of dye by the area under the dye concentration curve and multiply the result by 60:Cardiac output = (amount of dye / area under the curve)×60. The table below gives dye concentration for a dye-dilution cardiac output. The amount of dye injected was 8 mg. Sketch the graph and rectangles. Shade the area of approximation. Estimate the area under the curve and calculate the cardiac output from this estimate. Cardiac output?
5:24 PM Thu Jul 1
* 53% O
A cofc.brightspace.com
10
Time (s) after injection
Dye
concentration
t
8
7
4
2.5
5
8
8.
5
10
7
4
14
3
18
3
2
22
2
26
.5
30
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
-1
Use midpoints of the intervals and the width Ax=2, find area under the curve = sum of the area
of approximating rectangles.
Area under the curve =
4
| 4
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Transcribed Image Text:5:24 PM Thu Jul 1 * 53% O A cofc.brightspace.com 10 Time (s) after injection Dye concentration t 8 7 4 2.5 5 8 8. 5 10 7 4 14 3 18 3 2 22 2 26 .5 30 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 -1 Use midpoints of the intervals and the width Ax=2, find area under the curve = sum of the area of approximating rectangles. Area under the curve = 4 | 4
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