First, we can write the equation of the line using the information provided:
Now, we can create a table:
Finally, we can graph the line:
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:
10000π units²
Step-by-step explanation:
From the question given above, the following data were obtained:
Circumference (C) = 100π
Surface Area of sphere (SA) =?
Next, we shall determine the radius. This can be obtained as follow:
Circumference (C) = 100π
Radius (r) =?
C = 2πr
100π = 2πr
Divide both side by 2π
r = 100π / 2π
r = 50 units
Finally, we shall determine the surface area of the sphere. This can be obtained as follow:
Radius (r) = 50 units
Surface Area of sphere (SA) =?
SA = 4πr²
SA = 4 × π × 50²
SA = 4 × π × 2500
SA = 10000π units²
Therefore, the surface area of the sphere is 10000π units²
Answer:
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Step-by-step explanation:
Before leaving for work, Victor checks the weather report in order to decide whether to carry an umbrella. The forecast is “rain" with probability 20% and “no rain" with probability 80%. If the forecast is “rain", the probability of actually having rain on that day is 80%. On the other hand, if the forecast is “no rain", the probability of actually raining is 10%.
1. One day, Victor missed the forecast and it rained. What is the probability that the forecast was “rain"?
2. Victor misses the morning forecast with probability 0.2 on any day in the year. If he misses the forecast, Victor will flip a fair coin to decide whether to carry an umbrella. (We assume that the result of the coin flip is independent from the forecast and the weather.) On any day he sees the forecast, if it says “rain" he will always carry an umbrella, and if it says “no rain" he will not carry an umbrella. Let U be the event that “Victor is carrying an umbrella", and let N be the event that the forecast is “no rain". Are events U and N independent?
3. Victor is carrying an umbrella and it is not raining. What is the probability that he saw the forecast?
