I'm so confused about this question for homework . Could you help me? The glee club has 120 cupcakes to sell. They have decided
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The lines intersect at the point
Explanation:
The given two equations are and
We need to determine the whether that they intersect.
To determine the point of intersection, let us solve the equation by substitution method.
Let us equate both the equations.
Thus, we have,
Subtracting both sides by x, we get,
Simplifying, we have,
Dividing both sides by -3, we get,
Substituting in the equation
, we get,
Thus, the lines intersect at the points and
Hence, the lines intersect at the point
Polar and cartesian equation<h2>Initial explanation</h2>
<h2>STEP 2: secØ equation</h2>
<h2>STEP 3: comparison between given equation and secØ equation</h2>
Let's analyze the relation between r and x and y:
We have that between the indicated value of r (of the polar coordinates) and x and y (of the cartesian coordinates) there is a relation because they form a triangle. If r changes, then the value of x and y will change.
<h2>STEP 1: given equation</h2>Using the given equation
r = 2 secØ
we have that
Observing the image of the initial explanation we have a right triangle, we know that the equation of
secØ for any right triangle is given by:
In this case,
hypotenuse = r
adjacent side = x
then,
Then, we have that:
This means that:
Then,
x = 2
The equation in cartesian coordinates is x=2.
Answer: x=2