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Answer:
Emma's flight is farther from the airport
Step-by-step explanation:
Even without doing any detailed calculation, you can see on a graph that the larger turn Alice's flight makes keeps it closer to the airport.
Emma's flight is farther from the airport.
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The distance can be calculated using the Law of Cosines. The angle of interest is the supplement of the turn angle. Since the leg distances are the same in each case, the only variable affecting the distance from the airport is the angle measure. Again, the larger the turn, the shorter the distance from the airport. If T is the turn angle, the distance is ...
d² = 100² +50² -2·100·50·cos(180° -T)
d² = 12500 +10000·cos(T) . . . . . . . using cos(180°-T) = -cos(T)
d = 100√(1.25+cos(T))
For Alice's 70° turn, the distance is ...
d = 100√(1.25+0.342) ≈ 126.18 mi
For Emma's 50° turn, the distance is ...
d = 100√(1.25 +0.643) ≈ 137.58 mi
Emma's flight is farther from the airport.
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The law of cosines formula is ...
c² = a² +b² -2ab·cos(C)
where triangle sides are lengths a, b, c and angle C is opposite side c.
The first function is represented by the green line, while the second is represented by the orange line
<h3>What are piecewise functions?</h3>Piecewise functions are functions that have at least 2 sub functions, each of which have different intervals
The function is defined by
The first function in f(x) is defined by
See attachment for the graph of the first function
<h3>(b) Graph the second function</h3>The second function in f(x) is defined by
See attachment for the graph of the second function
Read more about piecewise functions at:
