With each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as "120 over 80" it is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by p (1) = 90 +40 sin (120nt) where p is the blood pressure in mmHg (millimeters of mercury) and / is the time in minutes after recording begins. (a) Find the period of the function and interpret the results. (b) Find the maximum and minimum values and interpret this as a blood pressure reading. (c) Find the times at which the blood pressure is at its maximum. Part 1 of 3
With each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as "120 over 80" it is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by p (1) = 90 +40 sin (120nt) where p is the blood pressure in mmHg (millimeters of mercury) and / is the time in minutes after recording begins. (a) Find the period of the function and interpret the results. (b) Find the maximum and minimum values and interpret this as a blood pressure reading. (c) Find the times at which the blood pressure is at its maximum. Part 1 of 3
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text:With each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called
the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as "120 over 80" it
is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by p (1) = 90+40 sin (120nt) where p is the
blood pressure in mmHg (millimeters of mercury) and t is the time in minutes after recording begins.
(a) Find the period of the function and interpret the results.
(b) Find the maximum and minimum values and interpret this as a blood pressure reading.
(c) Find the times at which the blood pressure is at its maximum.
Part 1 of 3
(a) Find the period of the function and interpret the results.
1
minutes and represents the time for one complete heartbeat.
60
The period is
This implies that the heart rate is
60 beats per minute. (Write your answers as simplified fractions, if necessary.)
Part 2 of 3
(b) Find the maximum and minimum values and interpret this as a blood pressure reading.
The maximum is
1 mmHg, the minimum is
mmHg and the blood pressure reading is
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