By applying the definition of continuity and knowing piecewise functions, we know that the solution to this system of linear equations is c = 10 and d = -8.
<h3>How to make a piecewise function continuous</h3>
According to the <em>functional</em> theory, functions are continuous for a given interval if and only if the function has an only value for each element of the interval. In the case of the <em>piecewise</em> function, we must observe these two conditions:
2 · x = c · x² + d, for x = 1 (1)
4 · x³ = c · x² + d, for x = 2 (2)
Then, we have the following system of linear equations:
c + d = 2 (1b)
4 · c + d = 32 (2b)
The solution to this system of linear equations is c = 10 and d = -8.
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Answer:
there are 36 cats in one house the ratio is 1:2
Step-by-step explanation:
Mr. Reed DATA:
rate = 40 mph ; time = x 4.5 hrs ; distance = 40x miles
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Mrs. Reed DATA:
rate = 60 mph ; time = x hrs ; distance = 60x - 210 miles
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Equation:
40x = 60x -210
-20x = -210
x = 10.5 hrs
x-3.5 = 7 hrs (Mr. Reed's time)
