How do I use the following cosine equation to get the Sinusoid Max & Min Times (x values), and Sinusoid Max and Min Values (
1 answer:
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Answer:
- maximum: (x, y) = (12.4n+3.2, 186.322)
- minimum: (x, y) = (12.4n+9.4, 163.498)
Step-by-step explanation:
You know that cos(α) is a maximum at α=0, 2π, 4π, and all even multiples of π. You know cos(α) is a minimum for α=π, 3π, 5π, and all odd multiples of π.
You can find your value of x at which y will be a maximum by setting the argument of the cosine function equal to zero (and/or 2nπ). If we use α=2nπ, then we have ...
α = (5π/31)(x -3.2) = 2nπ
(x -3.2) = (31/5)(2n) = 12.4n
Tidal maxima will occur at ...
x = 12.4n +3.2 . . . . . for integer values of n
Without bothering to go through the solution for α being odd multiples of π, we can see from this that the period is 12.4 hours. We know the tidal minimum will be half a period later, or 6.2 hours later than this.
Tidal minima will occur at ...
x = 12.4n +9.4 . . . . for integers n
__
Of course, cos(α) has extremes of ±1, so your tidal maximum will be ...
y = 11.412 +174.91 = 186.322
and your tidal minimum will be ...
y = -11.412 +174.91 = 163.498
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Answer:
With 99 % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints [19.91 miles, 31.49 miles] .
Step-by-step explanation:
<u>The complete question is</u>: In a random sample of six people, the mean driving distance to work was 25.7 miles and the standard deviation was 6.7 miles. Assuming the population is normally distributed and using the t-distribution, a 99% confidence interval for the population mean mu is left parenthesis 14.7 comma 36.7 right parenthesis (and the margin of error is 11.0).
Through research, it has been found that the population standard deviation of driving distances to work is 5.5 . Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, find the margin of error and construct a 99 % confidence interval for the population mean mu .
Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)
A. nothing % of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints.
B. With nothing % confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints.
C. It can be said that nothing % of the population has a driving distance to work (in miles) that is between the interval's endpoints.
D. With nothing % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints.
We are given that in a random sample of six people, the mean driving distance to work was 25.7 miles and the standard deviation was 6.7 miles.
Through research, it has been found that the population standard deviation of driving distances to work is 5.5 .
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean driving distance to work = 25.7 miles
= population standard deviation = 5.5 miles
n = sample of people = 6
= population mean driving distance to work
<em>Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation. </em>
<u>So, 99% confidence interval for the population mean, </u><u> is ;
</u>
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < < 2.58) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [19.91, 31.49]
Therefore, a 99% confidence for the population mean is [19.91, 31.49] .
The margin of error here is =
= = 5.793
With 99 % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints [19.91, 31.49] .
If you start by plotting your y-intercept (-8) then from there it’s rise over run (4/1) so you’ll go up four over one to the right. When graphing downwards (negative) from your y-intercept, go down four and left one.
