Answer:
The function for the outside temperature is represented by ![T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%2085%5C%C2%BA%20%2B%2015%5C%C2%BA%20%5Ccdot%20%5Csin%20%5Cleft%5B%5Cfrac%7Bt-6%5C%2Ch%7D%7B24%5C%2Ch%7D%20%5Cright%5D)
, where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
Mean temperature
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
![T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%20%5Cbar%20T%20%2B%20A%20%5Ccdot%20%5Csin%20%5Cleft%5B2%5Cpi%5Ccdot%5Cfrac%7Bt-6%5C%2Ch%7D%7B%5Ctau%7D%20%5Cright%5D)
Where:
- Mean temperature, measured in degrees.
- Amplitude, measured in degrees.
- Daily period, measured in hours.
- Time, measured in hours. (where t = 0 corresponds with 5 AM).
If , and 
, the resulting function for the outside temperature is:
Answer: 24:34
Step-by-step explanation:
If you multiply the ratio by 2, for example, it will still be equal.
2(2y-1)+y=3
y=1
x=2 x1 - 1
x=1
Answer:
the length of an arc = 10π ft.
Step-by-step explanation:
The length of an arc with angle Θ and radius r will be equal r * Θ
note the angle must be in radian
Given: Θ = 180° = π and radius = r = 10 ft.
<u>So, the length of the arc = π * 10 = 10π ft.</u>
Answer:
Percentage = 66%
Step-by-step explanation:
Let the number of students that pass be P.
Let the number of students that fail be F.
Given the following data;
Total number of students, T = 890 students
P = 300 students
To find the percentage that failed;
First of all, we would determine the number of students that failed using the mathematical expression given below;
Total students, T = P + F
890 = 300 + F
F = 890 - 300
F = 590
Percentage = 66.29 ≈ 66%
Therefore, the percentage of students that failed or didn't pass is 66%.
