Answer: 14 units.
Step-by-step explanation:
You can find arc length using the radius by this formula:
θ = , where s = the length of the arc and r = the radius.
So, your equation is
2 = s/7
Therefore, your arc length is 14 units.
Use the circle below to answer this question. Point P is at the center of the circle. What is the length of the circumference of
the circle, rounded to the nearest tenth of a centimeter? 14.1 centimeters 28.3 centimeters 63.6 centimeters 127.2 centimeters
1 answer:
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To solve the problem we must know about the equation of a circle and complex numbers.
<h2>Equation of circle</h2>Radius² = (Distance between the center and any point on the circle)²
Radius =
Complex Number, z = (x +iy)
Another point that will lay on the same circle is (12 + 10i).
<h2>Explanation</h2>Given to us
- center = (4 – 5i)
- point on the circle = (19 – 13i)
Solution
We know that equation for a circle can be written as,
<h3>Radius of the Circle </h3>Radius of the Circle
= √(Distance between the center and any point on the circle)²
Radius of the Circle = √[4-19]²+[-5 -(-13)]²
= √[-15]²+[8]²
= √225 + 64
= √225 + 64
= √289
= 17
Now compare the distance between the center of the circle and the points.
<h3>Comparison</h3>A.) –11 –3i
Distance between the center and point on the circle
= √[4-(-11)]² + [-5 - (-3)]²
= √[15]² + [-2]²
= √225 + 4
= √229
B.) –4. 5+3. 5i
Distance between the center and point on the circle
= √[4-(-4.5)]² + [-5 - (3.5)]²
= √[9.5]² + [-8.5]²
= √90.25+ 72.25
= √162.5
C.) 12 + 10i
Distance between the center and point on the circle
= √[4-(12)]² + [-5 - (10)]²
= √[-8]² + [-15]²
= √64+ 225
= √289
= 17
D.) 21 + 12i.
Distance between the center and point on the circle
= √[4-(21)]² + [-5 - (12)]²
= √[17]² + [-17i]²
= √289+ 289
= √578
Hence, another point that will lay on the same circle is (12 + 10i).
Learn more about Equation of Circle: