Take the derivative with respect to t

the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero

divide by w

we add sin(wt) to both sides

divide both sides by cos(wt)

OR

(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

since 2npi is just the period of cos

substituting our second soultion we get

since 2npi is the period

so the maximum value =

minimum value =
Answer:
37
Step-by-step explanation:
13 blue
24 green
Answer:
y = 1/2x + -3
Step-by-step explanation:
Answer/Step-by-step explanation:
Factor this. GCF=2
2(2cos2x+cos x-1)=0
2(2cos x -1)(cos x+1)=0 Set each factor equal to zero and solve
2cos x -1=0 Add 1 to both sides
2cos x =1 Divide by 2
cos x =1/2
x=π/3
x=5π/3
cos x+1=0 Subtract 1 from both sides
cos x=-1
<u><em>x = π</em></u>
<u><em></em></u>
Answer:
Step-by-step explanation:
From the information given,
Number of personnel sampled, n = 85
Mean or average = 6.5
Standard deviation of the sample = 1.7
We want to determine the confidence interval for the mean number of years that personnel spent in a particular job before being promoted.
For a 95% confidence interval, the confidence level is 1.96. This is the z value and it is determined from the normal distribution table. We will apply the following formula to determine the confidence interval.
z×standard deviation/√n
= 1.96 × 6.5/√85
= 1.38
The confidence interval for the mean number of years spent before promotion is
The lower end of the interval is 6.5 - 1.38 = 5.12 years
The upper end is 6.5 + 1.38 = 7.88 years
Therefore, with 95% confidence interval, the mean number of years spent before being promoted is between 5.12 years and 7.88 years