Back in the 1970s there was a fad called biorhythms People b

Back in the 1970s, there was a fad called “biorhythms”. People believed that their physical, emotional, and intellectual abilities could be modeled by the following equations:

In these equations, t represents the number of days a person has been alive. Biorhythm believers feared “critical days” on which one or more of the functions were equal to 0.
1) Find the expressions that would identify all the days a person would experience a critical day. (hint: there will be two expressions for each ability):

            a. Physically

            b. Emotionally

            c. Intellectually

2) How many emotional critical days will a person experience during the first three years of their life? (hint: create inequalities measuring in days)

3) When will a person experience their first critical day and for which ability?

4) Graph all 3 equations. For which ability will a person experience the most critical days? How do you know this? (hint: think in periods)

Since there are many combinations, you decide to solve this as a system.

Using the sum-to-product formulas, find a new equation to model the system. Reduce all fractions. Write the equation below.

7) According to the equation you found in question 5, what day of your life did you experience your first double critical day? Why is this wrong?

8) Why do you think the equation you found in question 5 generated that value? (hint: what does that equation represent? It’s not critical days.)

9) What does set P = {23k, 11.5 + 23k} for k ? 0 represent? What variable is this in our story?

10) What does set E = {28k, 14 + 28k} for k ? 0 represent? What variable is this in our story?

11) What does k represent? (hint: this is a hard one! Look at the graphs for help)

12) Does k = 0 generate the same t-values for each set?

13) If you are looking for “double critical days”, what are you looking for between the sets P and E?

14) Besides using the graph, identify when the first physical/emotional critical day is. Be sure to provide an explanation of how you found this day. (hint: it’s longer that 1.5 years, but less than 2 years)

15) The first physical/emotional critical day pattern will work for other combinations. When is the first physical/intellectual critical day? (hint: what do you notice about the common denominator from the expressions in question 5).

16) Believers lived in special fear of “triple critical days”. On which day of your life will you experience your first triple critical day?

CAN SOMEONE DO PHYSICAL, TO HELP ME get start and please show work thanks

Solution

1)
Physical :
sin(2pi*t/23) = 0
2pi*t/23 = n*pi
So, 2t/23 = n
t = 23*(n/2)

Emotionally :
2pi*t/28 = n*pi
t/14 = n
t = 14n

Intellectually :
sin(2pi*t/33) = 0
2pi*t/33 = n*pi
2t/33 = n
So, t = 33*(n/2)

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2)
3 years = 365*3 = 1095 days
14n <= 1095
n <= 1095/14
n= 78.2142857142857143
So, a person will experience 78 emotional critical days in three years

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3) First critical day :
The first critical say is when t = 23*n/2 ---> t = 23/2 or 11.5 days
So, the first critical day would be a physical one and will happen on 11.5th day

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4)
Time period of physical = 2pi / (2pi/23) = 23
Time period of emotional = 2pi / (2pi/28) = 28
Time period of intellectual = 2pi / (2pi/33) = 33
The one that has most frequency is physical because its time period is least
So, a person experiences physical critical days the most