In the theory of biorhythms a sine function of the form P(t)=50sin(ωt)+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: period 23 days.
Emotional potential: period 28 days.
Intellectual potential: period 33 days.
Find ω for each characteristic.
Calculation:
We have to find ω by using ω=2πT , Physical potential of period 23 days will be,
ω=2πTω=2π23
ω=2π23
Emotional potential for period 28 days.
ω=2πTω=2π28ω=π14
ω=π14
Intellectual potential for period 33 days.
ω=2πTω=2π33
Hence, ω is ω=2π23 , ω=π14 , ω=2π33 .
b.
To determine
Graph all tree functions on same graph.
b.
Expert Solution
Answer to Problem 93AYU
Explanation of Solution
Given information:
In the theory of biorhythms a sine function of the form P(t)=50sin(ωt)+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: period 23 days.
Emotional potential: period 28 days.
Intellectual potential: period 33 days.
Using graphing utility, graph all tree functions on same graph.
Calculation:
For Physical potential of period 23 days function will be ,
P(t)=50sin(2π23t)+50
For emotional potential for period 28 days function will be .
P(t)=50sin(π14t)+50
For Intellectual potential for period 33 days function will be.
P(t)=50sin(2π33t)+50
Graph of all functions will be,
Hence, the graph is drawn.
c.
To determine
Is there a time t when all the three characteristics have 100% potential? When it is?
c.
Expert Solution
Answer to Problem 93AYU
No
Explanation of Solution
Given information:
In the theory of biorhythms a sine function of the form P(t)=50sin(ωt)+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: period 23 days.
Emotional potential: period 28 days.
Intellectual potential: period 33 days.
Is there a time t when all the three characteristics have 100% potential? When it is?
Calculation:
No, there is no time t when all the three characteristics have 100% potential, because the given function P(t)=50sin(ωt)+50 have maximum value of 50% only as seen in the graph.
Hence, No, there is no time t when all the three characteristics have 100% potential.
d.
To determine
Describe your physical, emotional and intellectual potential for the next 30days .
d.
Expert Solution
Answer to Problem 93AYU
P1(t)=−66.168P2(t)=6.3P3(t)=−7.774
Explanation of Solution
Given information:
In the theory of biorhythms a sine function of the form P(t)=50sin(ωt)+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: period 23 days.
Emotional potential: period 28 days.
Intellectual potential: period 33 days.
Suppose that you are 20 years old today (t=7305days) . Describe your physical, emotional and intellectual potential for the next 30days .
Calculation:
Age is given as 20 years so that age function will be.
y=50sin(7305t)+50
Now find physical potential for next 30days with ω=2π23 will be,
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