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Complete Question
Major arc CBD measures 300°. Which is the radian measure of its corresponding central angle?
a)4pi/3 radians
b) 5pi/6 radians
c) 5pi/3 radians
d) 11pi/6 radians
Answer:
c) 5pi/3 radians = 5π/3 radians
Step-by-step explanation:
The corresponding central angle can be defined as the angle that is formed when there is a joining together of two radii at the center of the circle.
The circumference of a circle is given as
360° = 2πr
The major arc CBD is 300°
Therefore,
360° = 2πr , radius is not given hence , 360° = 2π
300° = Y (Unknown)
Cross multiply
360Y= (300× 2π)
Y = 600π ÷ 360
Y = (5π÷ 3) radians
Y = 5π/3 radians
Hence the radian measure for the corresponding angle is = 5π/3 radians
<span>1. The two boats picked for the trip are the steamboat and the tall ship. Let us assume that we will take the steamboat going to the island, and then we will take the tall ship for the return trip. We will then relate the distances travelled by both ships to each other.
2. We know that the steamboat takes five hours to complete the trip. The tall ship takes more time, at ten hours to complete the trip. We do not have the exact speeds of the steamboat or of the tall ship, but we do know that the tall ship is 10 knots slower than the steamboat. We likewise do not know the exact distance travelled by either ship, but we do know that both travel the same distance. We want to find out how fast each boat travels. We expect the answers to be in knots, with a difference of 10.
3. We know that distance is equivalent to the product of speed of a boat multiplied by the time of travel. For the trip going to the island, we will use the steamboat. Let its speed be x knots (equivalent to x nautical miles per hour), and let the distance going to the island be d nautical miles. Given that the time takes is 5 hours, this means that d = 5x.
4. If we let x be the speed of the
boat you are taking to the island (the steamboat), then we know that the speed of the other boat (the tall ship) is 10 knots less than the steamboat's. So the speed of the tall ship (for the return trip) is (x - 10) knots.
5. Similar to part 3: we will multiply speed by time to determine the distance from the island. From part 4, we have determined that the speed of the tall ship to be used in returning is (x - 10) knots. Meanwhile, the given in the problem says that the tall ship will take 10 hours to make the trip. Therefore the distance will be equal to d = 10(x - 10) = 10x - 100 nautical miles.
6. We can assume that the distance travelled going to the island is the same distance travelled coming back. Therefore, we can equate the formula for distance from part 3 for the steamboat, to the distance from part 5 for the tall ship.
5x = 10x - 100
7. Solving for x: 5x = 10x - 100
-5x = -100
x = 20
Since x is the speed of the steamboat, x = 20 means that the steamboat's speed is 20 knots.
8. We determined in part 4 that the speed of the second boat (in our case, the tall ship) is (x - 10) knots. Since we have calculated in part 7 that the steamboat travels at x = 20 knots, then the speed of the tall ship is (x - 10) = 20 - 10 = 10 knots.</span>
Answer:
In algebra, like terms are terms that have the same variables and powers.
Is that a question???????
We know that
if <span>points a and b lie on the circle and O is the center
so
OA is the radius
OA=OB
5x-11=4(x-1)-----> 5x-11=4x-4----> 5x-4x=11-4-----> x=7
OA=5x-11-------> OA=5*7-11-----> OA=24 units
the diameter is (OA+OB)
2*OA------> 2*24------> 48 units</span>
