Find the rate of change
2 answers:
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Answer: The intersection region shown in the graph attached is the solution of the system of inequalities.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
Given the following system of inequalities:
We need to graph the lines.
We have the line:
Solving for "y", we get:
Knowing that and
, we can graph it.
Since the symbol is , the line must be solid.
The other line is:
Since "x" only takes one value, we can identify that it is a vertical line, so we can graph it.
Since the symbol is , the line must be solid.
We need to substitute a point that is not on the line, into each inequalities. Let's choose the point (0,0).
Then:
This is false, therefore, we must shade the half that does not contain this point.
This is false, so we must shade the half that does not contain this point.
The intersection region of the solutions (Observe the graph attached) of the given inequalities is the solution of the system of inequalities.
9514 1404 393
Answer:
31.243 units
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles in a right triangle. Using the attached figure, it is convenient to find the length of BE as an intermediate step in the solution.
Sin = Opposite/Hypotenuse
sin(30°) = BE/100
BE = 100·sin(30°)
Then ...
Tan = Opposite/Adjacent
tan(58°) = BE/x
x = BE/tan(58°) = 100·sin(30°)/tan(58°)
x ≈ 31.243 . . . . units
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<em>Comment on the figure</em>
The intermediate problem in creating the figure was to locate point D. That was accomplished by locating point C on a line at an angle of 58° CCW from the horizontal, using point B as a center. Then D is the intersection of BC with the x-axis. BE is drawn perpendicular to the x-axis.
