How many rational numbers are there between 2 and 20? Explain how you know.
2 answers:
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Answer: graph E.
A geometric sequence can be written as:
where:
a₁ = first term = 4
r = ratio = 0.5
Substituting the numbers, we have:
or else
This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).
In order to choose between graph B and E, let's evaluate the function in two different points:
Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.
The figure is shown below
From the figure
Angle 150 degree and angle p forms angles on a straight
Since the sum of angles on a straight line equals 180 degrees
Hence
Solve for p in the equation
Hence, p = 30
From the figure
Angle p and angle q are vertically opposite angles
Since vertically opposite angles are equal then
Hence, q = 30
Applying the rule of angles on a straight line
This implies
Substitute q = 30 into the equation
Solve for w
Hence, w = 90
