Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
2 answers:
By graphing the given equation
<span>r = 4 - 3 sin θ
We find that </span><span>the graph is symmetric about the y-axis
The graph of the given equation is attached below
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Some information about the given equation:
the given equation is like the form of the </span>Cardioid
A curve that is somewhat heart shaped. A cardioid can be drawn by tracing the path of a point on a circle as the circle rolls around a fixed circle of the same radius. The equation is usually written in polar coordinates.
Equations of Cardioid:
<span>r = 4 - 3 sin θ
We find that </span><span>the graph is symmetric about the y-axis
The graph of the given equation is attached below
------------------------------------------------------------------------------
Some information about the given equation:
the given equation is like the form of the </span>Cardioid
A curve that is somewhat heart shaped. A cardioid can be drawn by tracing the path of a point on a circle as the circle rolls around a fixed circle of the same radius. The equation is usually written in polar coordinates.
Equations of Cardioid:
r = a ± a cos θ (horizontal) or <span>r = a ± a sin θ (vertical)</span>
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Answer:
C. (see the attachment)
Step-by-step explanation:
Both inequalities include the "or equal to" case, so both boundary lines will be solid. That excludes choices A and D.
The first inequality is plotted the same way in all graphs, so we must look at the second inequality. The relationship of y and the comparison symbol is ...
-y ≥ (something)
If we multiply by -1, we get ...
y ≤ (something else)
This means the solution space will be <em>on or below (less than or equal to) the boundary line</em>. This is the shaded area in graph C. (Graph B shows shading <em>above</em> the line.)
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<em>Further comment</em>
Since the boundary for the second inequality is fairly steep, "above" and "below" the line can be difficult to see. Rather, you can consider the relationship of x to the comparison symbol. For the second inequality, that is ...
x ≥ (something)
indicating the solution space is <em>on or to the right of the boundary line</em>.
