Answer:

Step-by-step explanation:
Consider linear differential equation 
It's solution is of form
where I.F is integrating factor given by
.
Given: 
We can write this equation as 
On comparing this equation with
, we get 
I.F =
{ formula used:
}
we get solution as follows:

{ formula used:
}
Applying condition:

So, we get solution as :

Answer: 1.75hours or 1.45
Step-by-step explanation:
4
6
Cause 4 times 1 and 2 times 2
Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92