Answer:
The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)
Step-by-step explanation:
The cosine function equation is given as follows h = d + a·cos(b(x - c))
Where:
= Amplitude
2·π/b = The period
c = The phase shift
d = The vertical shift
h = Height of the function
x = The time duration of motion of the wave, t
The given data are;
The amplitude = 2 feet
Time for the wave to pass the dock
The number of times the wave passes a point in each cycle = 2 times
Therefore;
The time for each complete cycle = 2 × 30 seconds = 60 seconds
The time for each complete cycle = Period = 2·π/b = 60
b = π/30 =
Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have
h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)
The cosine function is h = 2·cos((π/30)·t).
Answer:
33/7
Step-by-step explanation:
Answer:
The claim is false.
Step-by-step explanation:
Given the data :
13 24 21 37 15 25 18 22 40 32
The sample mean and standard deviation can ben calculated for the given sample.
Using calculator :
Sample mean, xbar = 24.7
Sample standard deviation, s = 9.04
Sample size, n = 10
The hypothesis :
H0 : μ = 17
H1 : μ ≠ 17
The test statistic :
(xbar - μ) ÷ (s/√(n))
(24.7 - 17) ÷ (9.04/√(10))
7.7 / 2.8586990
Test statistic = 2.694
We can obtain the Pvalue, at α = 0.05 ; df = n-1 = 9
Pvalue = 0.0246
Since Pvalue < α ; we reject the null ; Hence, there is significant evidence to conclude that an adult American does not spend average of 17 hours in leisure
Answer:
17/13
Step-by-step explanation:
r(6) = 3(6) - 1 = 17 and s(6) = 2(6) + 1 = 13.
Then (r/s)(6) = 17/13.
Answer:
x = 15
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
3+6x + 5x+12 = 180
Combine like terms
11x+15 = 180
Subtract 15 from each side
11x+15-15 =180-15
11x = 165
Divide by 11
11x/11 =165/11
x =15
