Answer:
2 cookies
Step-by-step explanation:
let c represent cookies, m represent muffins. set up a system of equations:
2c+3m=16
m=2c
(the top equation shows that cookies are $2 each, and muffins are $3, and that the total cost is $16. the bottom equation shows that Lori bought twice as many muffins as cookies).
then solve the system of equations by substitution, substituting 2c for m in the top equation:
2c+3(2c)=16
2c+6c=16
8c=16
c=2
this means that lori bought 2 cookies.
For this case we use the following formula
Area of Sector = Area * radians of sector / 2 * pi radians
Where,
Area: it is the area of the complete circle.
We have then:
Area = pi * r ^ 2
Area = pi * (6) ^ 2
Area = 36pi
Substituting values:
5pi = 36pi * radians of sector / 2 * pi
Clearing:
radians of sector = ((5pi) * (2pi)) / (36pi)
radians of sector = (10pi ^ 2) / (36pi)
radians of sector = (10pi) / (36)
radians of sector = (10/36) pi
radians of sector = (5/18) pi
in degrees:
(5/18) pi * (180 / pi) = 50 degrees
Answer:
The measure of the central angle is:
50 degrees
