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Answer:
The maximum number of packages that can be made with each package have same number of each item is = 6
Step-by-step explanation:
Given:
Mr. Harris has 48 pencils and 30 notebooks.
To find the number of packages he can make with each package have same number of each item.
Solution:
Number of pencils = 48
Number of notebooks = 30
In order to find the number of packages he can make with each package have same number of each item, we will find the greatest common factor of the given numbers.
<em>To find the G.C.F., we will list down the prime factors of each.</em>
We find that the G.C.F. = = 6
Thus, the maximum number of packages that can be made with each package have same number of each item is = 6
1. I suppose the ODE is supposed to be
Solving for gives
which is undefined when . The interval of validity depends on what your initial value is. In this case, it's
, so the largest interval on which a solution can exist is
.
2. Separating the variables gives
Integrate both sides. On the left, we have
where we substituted - or
- and
- or
.
On the right, we have
So
I'll leave the solution in this form for now to make solving for easier. Given that
, we get
and so our solution is