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Answer: t = - 5 ∈ = ( -∞ , -4 )
Step-by-step explanation:
The standard form of O.D.E is written as :
+
Equation given :
+
=
,
The first thing to do is to write the O.D.E in standard form , that is we will divide through by , so we have
With this , we can see that and
are both continuous in the same domain. Therefore , the intervals are :
= ( -∞ , -4 )
= ( - 4 , 4 )
= ( 4 , -∞ )
recall that y(−5) = 1 , then t = -5
This means that :
t = - 5 ∈ = ( -∞ , -4 )
Before we can determine the rectangular coordinate of the point, let's determine first its polar coordinates. For this, we need two things: radius and angle.
For the radius, we see that point R is 4 units away from the center.
For the angle, we see that it is 30° clockwise or 330° counterclockwise. See the illustration below:
Now that we know the radius is 4 units and the angle is 330° counterclockwise, let's now convert this to rectangular coordinates.
Use the formula below:
For x-coordinate, we have:
For the y-coordinate, we have:
Therefore, the rectangular coordinate of the given polar point is (2√3, -2). Option B.
