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 the diastolic pressure. When a doctor records an individual’s blood pressure such as "120 over 80,â€� it is understood as "systolic over diastolic." Suppose that the blood pressure for a certain individual is approximated by p t = 90 + 20 sin 140 π t 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.
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 the diastolic pressure. When a doctor records an individual’s blood pressure such as "120 over 80,â€� it is understood as "systolic over diastolic." Suppose that the blood pressure for a certain individual is approximated by p t = 90 + 20 sin 140 π t 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.
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 the 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
t
=
90
+
20
sin
140
π
t
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.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
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