If the circumference of the circle below is 90, what is the length of the minor arc)? 609 A. 90 B. 15 C. 30 D. 10
1 answer:
Answer:
arc XY = 15 units
Step-by-step explanation:
<u>GIVEN :-</u>
- Angle subtended by arc XY at center = 60°
- Circumference of the circle = 90 units.
<u>TO FIND :-</u>
- Length of XY
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
Length of arc of the sector = where θ is the angle subtended by arc of the sector at the center of the circle.
<u>SOLUTION :-</u>
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Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
and on the right we will just add 10 and 2:
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}