Determine the number of solutions to the following system of equations.
2 answers:
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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>
When we find a geometric sequence using the first and second terms, what we do is divide the second by the first to find a "common ratio," the number you multiply by to get to the next term.
In this case, we only have the second and fifth terms. From the second to the fifth term, we've multiplied by that common ratio three times.
What we can do is divide the fifth by the second and then take the <em>cube root</em> to find our common ratio.
![2304\div-36=-64\\\sqrt[3]-64=\boxed{-4}](https://tex.z-dn.net/?f=2304%5Cdiv-36%3D-64%5C%5C%5Csqrt%5B3%5D-64%3D%5Cboxed%7B-4%7D)
Now we know we're multiplying by -4 each time, let's find the first term.
The opposite of multiplying by -4 would be dividing by -4. We work back from our second term -36 to find that the first term would be 9.
For each sucessive term, we then multiply by -4.
Our equation is
In this case, we only have the second and fifth terms. From the second to the fifth term, we've multiplied by that common ratio three times.
What we can do is divide the fifth by the second and then take the <em>cube root</em> to find our common ratio.
Now we know we're multiplying by -4 each time, let's find the first term.
The opposite of multiplying by -4 would be dividing by -4. We work back from our second term -36 to find that the first term would be 9.
For each sucessive term, we then multiply by -4.
Our equation is