ans=a.34 students,b.12m
Step-by-step explanation: a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.
Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:
The total number of students who offer at least one subject is 35 + 28 + 15 = 78
The number of students who offer Biology and Economics is 12
The number of students who offer Biology and Physics is 7
The number of students who offer Economics and Physics is 5
So the number of students who offer all three subjects is given by:
35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34
Therefore, 34 students offer all three subjects.
b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.
Each interior angle of a regular polygon with n sides is given by:
angle = (n-2) * 180 / n
So for a regular polygon with (2m + 1) sides, we have:
1440 = (2m + 1 - 2) * 180 / (2m + 1)
Expanding and simplifying:
1440 = 360m / (2m + 1)
Multiplying both sides by (2m + 1):
1440 * (2m + 1) = 360m
Expanding the left side:
2880 + 1440 = 360m
4320 = 360m
Finally, dividing both sides by 360:
m = 12
Therefore, the value of m is 12.