In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the percent. P of a person's potential at time t, where t is measured in days and t=0 is the person's birthday. Three characteristics are commonly measured: physical potential with a period of 23 days, emotional potential with a period of 28 days, and intellectual potential with a period of 33 days. Co (a) Find for each characteristic. 2x For physical potential, co 23 (Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the expression.) For emotional potential, (Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the expression.) 2t For intellectual potential, (Simplify your answer. Type an exact answer in terms of r. Use integers or fractions for any numbers in the expression.) (b) Using a graphing utility, graph all three functions on the same screen. Choose the correct answer below. All graphs are shown in [0,50,10] by [0,100,10] viewing windows. OA OC XXXX XXXX² M₁ XXX M (c) Is there a time t when all three characteristics have 100% potential? When is it? A. Yes, t No (d) Suppose that a person is 44 years old today (t = 16,071 days). Describe this person's physical, emotional, and intellectual potential for the next 30 days. The next time this person's physical potential peaks is days after the person's birthday. (Round up to the nearest day.)
In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the percent. P of a person's potential at time t, where t is measured in days and t=0 is the person's birthday. Three characteristics are commonly measured: physical potential with a period of 23 days, emotional potential with a period of 28 days, and intellectual potential with a period of 33 days. Co (a) Find for each characteristic. 2x For physical potential, co 23 (Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the expression.) For emotional potential, (Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the expression.) 2t For intellectual potential, (Simplify your answer. Type an exact answer in terms of r. Use integers or fractions for any numbers in the expression.) (b) Using a graphing utility, graph all three functions on the same screen. Choose the correct answer below. All graphs are shown in [0,50,10] by [0,100,10] viewing windows. OA OC XXXX XXXX² M₁ XXX M (c) Is there a time t when all three characteristics have 100% potential? When is it? A. Yes, t No (d) Suppose that a person is 44 years old today (t = 16,071 days). Describe this person's physical, emotional, and intellectual potential for the next 30 days. The next time this person's physical potential peaks is days after the person's birthday. (Round up to the nearest day.)
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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In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the
percent P of a person's potential at time t, where t is measured in days and t=0 is the person's
birthday. Three characteristics are commonly measured: physical potential with a period of 23
days, emotional potential with a period of 28 days, and intellectual potential with a period of 33
days.
(a) Fing for each characteristic. Recall that the period of the sine function in way is given by CO
2x
Since the period of physical potential is 23 days, solve 23 for 0.
2π
-=23
2m = 2300
2π
23
= 00
Find for emotional potential similarly, using the period of 28 days.
2m
-28
00
2= 280
2m
28
*
14
Find for intellectual potential similarly, using the period of 33 days.
2n
33
= 00
33
2π = 3300
2m
Multiply both sides by
Divide both sides by 23.
= 00
(b) Using a graphing utility, graph all three functions on the same screen. The correct graph is
shown below in a [0,50,10] by [0,100,10] viewing window.
M
(c) Since the periods 23, 28, and 33 are relatively prime, there is not a time t when all three
characteristics have 100% potential.
(d) Suppose that a person is 52 years old today (t = 18,993 days). Describe this person's physical,
emotional, and intellectual potential for the next 30 days. To examine behavior, set the values
Xmin = 18,993 and Xmax = 19,023 on a graphing calculator.
Now use the maximum function of the graphing calculator to find the time that each potential
peaks.
The next time this person's physical potential peaks is 11 days after the person's birthday.
The next time this person's emotional potential peaks is 26 days after the person's birthday.
The next time this person's intellectual potential peaks is 24 days after the person's birthday.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a8023c3-c690-4e2c-b9f1-72fb581950b4%2F2fd101f6-411f-44ff-be22-1a16c45e6c37%2F4q05j31_processed.jpeg&w=3840&q=75)
Transcribed Image Text:View an example | All parts showing
In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the
percent P of a person's potential at time t, where t is measured in days and t=0 is the person's
birthday. Three characteristics are commonly measured: physical potential with a period of 23
days, emotional potential with a period of 28 days, and intellectual potential with a period of 33
days.
(a) Fing for each characteristic. Recall that the period of the sine function in way is given by CO
2x
Since the period of physical potential is 23 days, solve 23 for 0.
2π
-=23
2m = 2300
2π
23
= 00
Find for emotional potential similarly, using the period of 28 days.
2m
-28
00
2= 280
2m
28
*
14
Find for intellectual potential similarly, using the period of 33 days.
2n
33
= 00
33
2π = 3300
2m
Multiply both sides by
Divide both sides by 23.
= 00
(b) Using a graphing utility, graph all three functions on the same screen. The correct graph is
shown below in a [0,50,10] by [0,100,10] viewing window.
M
(c) Since the periods 23, 28, and 33 are relatively prime, there is not a time t when all three
characteristics have 100% potential.
(d) Suppose that a person is 52 years old today (t = 18,993 days). Describe this person's physical,
emotional, and intellectual potential for the next 30 days. To examine behavior, set the values
Xmin = 18,993 and Xmax = 19,023 on a graphing calculator.
Now use the maximum function of the graphing calculator to find the time that each potential
peaks.
The next time this person's physical potential peaks is 11 days after the person's birthday.
The next time this person's emotional potential peaks is 26 days after the person's birthday.
The next time this person's intellectual potential peaks is 24 days after the person's birthday.
![In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the percent
P of a person's potential at time t, where t is measured in days and t=0 is the person's birthday. Three
characteristics are commonly measured: physical potential with a period of 23 days, emotional potential
with a period of 28 days, and intellectual potential with a period of 33 days.
(a) Find for each characteristic
For physical potential, co
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the
expression.)
2x
For emotional potential, =
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the
expression.)
CIT
2t
33
(Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the
expression.)
For intellectual potential, >=
(b) Using a graphing utility, graph all three functions on the same screen. Choose the correct answer
below. All graphs are shown in [0,50,10] by [0,100,10] viewing windows.
OA
O.B.
Q
XXXX XXXX² M ₁
Yes; t =
(c) is there a time t when all three characteristics have 100% potential? When is it?
B. No
VXXXX
(d) Suppose that a person is 44 years old today (t = 16,071 days). Describe this person's physical,
emotional, and intellectual potential for the next 30 days.
The next time this person's physical potential peaks is days after the person's birthday.
(Round up to the nearest day.)
Q](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a8023c3-c690-4e2c-b9f1-72fb581950b4%2F2fd101f6-411f-44ff-be22-1a16c45e6c37%2F97icq3c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the theory of biorhythms, a sine function of the form P(t) = 50 sin (t) + 50 is used to measure the percent
P of a person's potential at time t, where t is measured in days and t=0 is the person's birthday. Three
characteristics are commonly measured: physical potential with a period of 23 days, emotional potential
with a period of 28 days, and intellectual potential with a period of 33 days.
(a) Find for each characteristic
For physical potential, co
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the
expression.)
2x
For emotional potential, =
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the
expression.)
CIT
2t
33
(Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the
expression.)
For intellectual potential, >=
(b) Using a graphing utility, graph all three functions on the same screen. Choose the correct answer
below. All graphs are shown in [0,50,10] by [0,100,10] viewing windows.
OA
O.B.
Q
XXXX XXXX² M ₁
Yes; t =
(c) is there a time t when all three characteristics have 100% potential? When is it?
B. No
VXXXX
(d) Suppose that a person is 44 years old today (t = 16,071 days). Describe this person's physical,
emotional, and intellectual potential for the next 30 days.
The next time this person's physical potential peaks is days after the person's birthday.
(Round up to the nearest day.)
Q
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