The correct answer is B) 9 m.
The measure of the sector of circle R is 32π/9 m. The measure of the central angle is 80°. This means that the sector is 80/360 = 2/9 of the circle. The area of a circle is given by A=πr², so the area of the sector is A=2/9πr². To verify this, 2/9π(4²) = 2/9π(16) = 32π/9.
Using this same formula for circle S, we will work backward to find the radius:
18π = 2/9πr²
Multiply both sides by 9:
18*9π = 2πr²
162π = 2πr²
Divide both sides by 2π:
162π/2π = 2πr²/2π
81 = r²
Take the square root of both sides:
√81 = √r²
9 = r
This is essentially asking how many different ways to partition 6 into 3 segments.
I am assuming "no ball in a box" is not allowed.
6 can be partitioned as
(4,1,1), (3,2,1), and (2,2,2)
So, calculate each partition, we get
(6 choose 4) + (6 choose 3)*(3 choose 2) + (6 choose 2) * (4 choose 2)
= 15 + 20*3 + 15*6
=165
The distance between the points (d) is found using the Pythagorean theorem.
Imagine the two points as defining the hypotenuse of a right triangle. The lengths of the legs of the triangle are the horizontal distance between the points and the vertical distance between the points. The the theorem tells us
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65 ≈ 8.1
The distance between the points is
C 8.1_____
You know that the distance must be longer than the longest leg (7) and must be shorter than the sum of the two legs (4+7=11). The only answer choice between 7 and 11 is 8.1.
Answer:
It takes 33 hours to produce 66 cars.
Step-by-step explanation:
When dividing 220 workers buy the amount of cars produced the amount of time spent on making 66 cars is 33 hours.
Easier Explaination:
Divide the amount of workers to the cars produced to find out how many hours it takes.