Question 1-3
1 answer:
Answer:
1/3
Step-by-step explanation:
The average rate of change of a function f(x) on an interval [a, b] is given by the formula ...
rate of change = (f(b) -f(a))/(b -a)
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For the given function and interval, this is ...
(log₂(4·8) -log₂(4·2))/(8 -2) = (5 -3)/(6) = 1/3
The average rate of change is 1/3.
_____
In the attached graph, the line between the points at the ends of the interval can be seen to have a rise of 1 for a run of 3. Its slope is 1/3.
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If we say that side "a" is the shortest (adjacent), side "b" is the second shortest (opposite), and side "c" is the longest (hypotenuse): then angle A would be 30°, angle B would be 60°, and angle C would be 90°
tan B = b/a
or
a tan B = b
they have 4 as the smallest value in all four options, so we know that a=4
4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3
that leaves two options left, so now we find "c":
c^2 = (a^2) + (b^2)
OR
so a=4, b=4√3, and c=8
Making your answer B
tan B = b/a
or
a tan B = b
they have 4 as the smallest value in all four options, so we know that a=4
4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3
that leaves two options left, so now we find "c":
c^2 = (a^2) + (b^2)
OR
so a=4, b=4√3, and c=8
Making your answer B