Please help me. When you have your blood pressure measured during a physicalexam

Question

Please help me. When you have your blood pressure measured during a physicalexamination, the nurse or doctor will record two numbers as aratio-for example, 120/80. The first number(systolic pressure) represents the amount ofpressure in the blood vessels when the heart contracts(beats) andpushes blood through the circulatory system. The second number(diastolic pressure) represents thepressure in the blood vessels at the lowest point between theheartbeats, when the heart is at rest. Acconding to the NationalInstitutes of Health, normal blood pressure is below 120/80,moderately high is fron 140/90 to 159/99, and severe is higher than160/100. The blood presure of a particular person is modeledapproximately by Where P is pressure in millimeters of mercury t seconds afterthe heart contracts. (A) Express the person's blood pressure as anappropriate ratio of two numbers. Explain how you arrived at thesenumbers. (B) What is the period of the heartbeat? (C) What is the pulse rate in beats per minute? Show yourcompulation.

Explanation / Answer

The formula given describes the pressure of a person. The systolic pressure is the maximum one (when the heartcontracts) occurs when cosine reaches its maximum value which is 1.Then P = 135 + 30(1) = 165 The diastolic pressure is the minimum one, it occurs whencosine reaches its minimum value which is -1. Then P = 135 + 30(-1) = 105 The pressure of this person is 165 / 105. Period T is found as the period of cosine (2) divided bythe coefficient before the variable (t in our case). T = 2 /(2.5) T = 0.8 seconds (The heart completes one cycle from one beatto another in 0.8 sec) The pulse is the number of beats in one minute = 60 sec. Pulse= 60 sec / Period = 60 / 0.8 = 75 beats For the last question you should use a graphing utility. Tofind the ratio of the preassure, take a max point and a minpoint.

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