1. The average monthly temperature, T, in degrees Celsius, in the Kawartha Lakes was modelled by T(t)=-22 cos(30t)° +10, where t represents the number of months. For t= 0, the month is January; for t= 1, the month is February, and so on. a) What is the period? Explain the period in the context of the problem. b) What is the range of temperatures for this model? 2. Each person's blood pressure is different, but there is a range of blood pressure values that is considered healthy. The function P(t) = -20 cos(300t)° +100 models the blood pressure, P (in millimetres of mercury), at time, t (in seconds), of a person at rest. a) What is the period of the function? What does the period represent for an individual? b) How many times does this person's heart beat each minute? c) Sketch the graph of y= P(t) for 0≤t≤6 d) What is the range of the function? Explain the meaning of the range in term of a person's blood pressure.
1. The average monthly temperature, T, in degrees Celsius, in the Kawartha Lakes was modelled by T(t)=-22 cos(30t)° +10, where t represents the number of months. For t= 0, the month is January; for t= 1, the month is February, and so on. a) What is the period? Explain the period in the context of the problem. b) What is the range of temperatures for this model? 2. Each person's blood pressure is different, but there is a range of blood pressure values that is considered healthy. The function P(t) = -20 cos(300t)° +100 models the blood pressure, P (in millimetres of mercury), at time, t (in seconds), of a person at rest. a) What is the period of the function? What does the period represent for an individual? b) How many times does this person's heart beat each minute? c) Sketch the graph of y= P(t) for 0≤t≤6 d) What is the range of the function? Explain the meaning of the range in term of a person's blood pressure.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. The average monthly temperature, T, in degrees Celsius, in the Kawartha Lakes was modelled by
T(t) = -22 cos(30t)° +10, where t represents the number of months. For t = 0, the month is
January; for t = 1, the month is February, and so on.
a) What is the period? Explain the period in the context of the problem.
b) What is the range of temperatures for this model?
2. Each person's blood pressure is different, but there is a range of blood pressure values that is
considered healthy. The function P(t) = -20 cos(300t)° +100 models the blood pressure, P (in
millimetres of mercury), at time, t (in seconds), of a person at rest.
a) What is the period of the function? What does the period represent for an individual?
b) How many times does this person's heart beat each minute?
c) Sketch the graph of y = P(t) for 0≤ t ≤6
d)
What is the range of the function? Explain the meaning of the range in term of a person's blood
pressure.
3. The depth of water, d(t) metres, in a seaport can be approximated by the sine function
d(t)=2.5 sin [29.52(t-1.5)] +13.4, where t is the time in hours.
a) Graph the function for 0≤ t ≤ 24 using a graphing calculator.
b) Find the period, to the nearest tenth of an hour.
c) A cruise ship needs a depth of at least 12 m of water to dock safely. For how many hours in
each period can the ship dock safely? Round your answer to the nearest tenth of an hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9c83688-7a75-495f-88bf-43c5d4f97a48%2F80435286-885e-4a60-a615-264d8a00006d%2Frcimtc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The average monthly temperature, T, in degrees Celsius, in the Kawartha Lakes was modelled by
T(t) = -22 cos(30t)° +10, where t represents the number of months. For t = 0, the month is
January; for t = 1, the month is February, and so on.
a) What is the period? Explain the period in the context of the problem.
b) What is the range of temperatures for this model?
2. Each person's blood pressure is different, but there is a range of blood pressure values that is
considered healthy. The function P(t) = -20 cos(300t)° +100 models the blood pressure, P (in
millimetres of mercury), at time, t (in seconds), of a person at rest.
a) What is the period of the function? What does the period represent for an individual?
b) How many times does this person's heart beat each minute?
c) Sketch the graph of y = P(t) for 0≤ t ≤6
d)
What is the range of the function? Explain the meaning of the range in term of a person's blood
pressure.
3. The depth of water, d(t) metres, in a seaport can be approximated by the sine function
d(t)=2.5 sin [29.52(t-1.5)] +13.4, where t is the time in hours.
a) Graph the function for 0≤ t ≤ 24 using a graphing calculator.
b) Find the period, to the nearest tenth of an hour.
c) A cruise ship needs a depth of at least 12 m of water to dock safely. For how many hours in
each period can the ship dock safely? Round your answer to the nearest tenth of an hour.
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