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A person’s blood pressure, p, in millimeters of mercury (mm Hg) is given, for t in seconds, by p = 100 + 20 sin(2.5πt). (a) What are the maximum and minimum values of blood pressure? (b) What is the interval between successive maxima? (c) Show your answers on a graph of blood pressure against time.

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Related Question

(a) A person's blood pressure is measured to be 120 ± 2 mm Hg . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?

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Answer:

Given equation:

p = 100 + 20 sin(2.5πt)

Part (a)

As:        -1 ≤ sin(x) ≤ 1

Then:   -1 ≤ sin(2.5πt) ≤ 1

So:       -20 ≤ 20 sin(2.5πt) ≤ 20

Therefore:

Maximum value = 100 + 20 = 120

Minimum value = 100 - 20 = 80

Part (b)

The interval between successive maxima is the period.

The period is 2π/B  where B is the coefficient of the independent variable.

⇒ Period = 2π ÷ 2.5π = 0.8

Part (c)

Attached

[Note - you do not need to add the period show in red on the graph when drawing the graph.  This has been added to prove part (b)]

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