Perform the indicated operation.(3x - 4)2
2 answers:
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Answer:
It is continuous since
Step-by-step explanation:
We are given that the function is defined as follows and
and we want to check the continuity in the interval [-4,5]. Note that this a piecewise function whose only critical point (that might be a candidate of a discontinuity) x=0 since at this point is where the function "changes" of definition. Note that 9-x and 9+12x are polynomials that are continous over all
. So F is continous in the intervals [-4,0) and (0,5]. To check if f(x) is continuous at 0, we must check that
(this is the definition of continuity at x=0)
Note that if x=0, then f(x) = 9-x. So, f(0)=9. On the same time, note that
. This result is because the function 9-x is continous at x=0, so the left-hand limit is equal to the value of the function at 0.
Note that when x>0, we have that f(x) = 9+12x. In this case, we have that
. As before, this result is because the function 9+12x is continous at x=0, so the right-hand limit is equal to the value of the function at 0.
Thus, , so by definition, f is continuous at x=0, hence continuous over the interval [-4,5].
Answer:
Option B.
Step-by-step explanation:
step 1
Find the central angle of the shaded sector
Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)
so
Let
x -----> the measure of the central angle of the shaded sector
∠x+72°=180°
∠x=180°-72°=108°
step 2
Find the area of the circle
The area of the circle is
we have
assume
substitute
step 3
Find the area of the shaded sector
Remember that the area of the complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 108 degrees