Question 1208108
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Piecewise functions can be a strange beast. 
I think of them as a Frankenstein's monster because we glue together various parts of other functions. 


The function will change its identity based on what the input is.
The input in this case is variable v (t is the parameter and appears to be fixed to t = 10).


We have 3 scenarios<ul><li>If 0 <= v < 1.79, then W(v) = t</li><li>If 1.79 <= v <= 20, then W(v) = 33 - (10.45 + 10*sqrt(v) - v)*(33-t)/22.04</li><li>If v > 20, then W(v) = 33 - 1.5958(33-t)</li></ul>-------------------------------------------------------------------------


Part (a)


t = 10
v = 5


v = 5 fits the interval 1.79 <= v <= 20, so we use the middle piece.


W(v) = 33 - (10.45 + 10*sqrt(v) - v)*(33-t)/22.04
W(5) = 33 - (10.45 + 10*sqrt(5) - 5)*(33-10)/22.04
W(5) = 3.977965752044
W(5) = 3.98
The wind chill is approximately 3.98 degrees Celsius.


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Part (b)


This time we have
t = 10
v = 25


v = 25 fits the interval v > 20 aka 20 < v < infinity.
So we'll use the 3rd piece of this piecewise function.


W(v) = 33 - 1.5958(33-t)
W(25) = 33 - 1.5958(33-10)
W(25) = -3.7034
The wind chill is roughly -3.7034 degrees Celsius.



Side notes:
10 degrees Celsius = 50 degrees Fahrenheit
3.98 degrees Celsius = 39.164 degrees Fahrenheit
-3.7034 degrees Celsius = 25.33388 degrees Fahrenheit
5 m/s = 18 km/hr = 11.1846815 mph
25 m/s = 90 km/hr = 55.9234073 mph
The decimal values are approximate.
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