It looks like the differential equation is

Check for exactness:

As is, the DE is not exact, so let's try to find an integrating factor <em>µ(x, y)</em> such that

*is* exact. If this modified DE is exact, then

We have

Notice that if we let <em>µ(x, y)</em> = <em>µ(x)</em> be independent of <em>y</em>, then <em>∂µ/∂y</em> = 0 and we can solve for <em>µ</em> :

The modified DE,

is now exact:

So we look for a solution of the form <em>F(x, y)</em> = <em>C</em>. This solution is such that

Integrate both sides of the first condition with respect to <em>x</em> :

Differentiate both sides of this with respect to <em>y</em> :

Then the general solution to the DE is

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a
levacccp [35]
Answer:

Step-by-step explanation:
Given
--- outcomes
-- sample size
Required

This is calculated as:

because none of the outcomes is greater than 12:
So:


Answer:
1
Step-by-step explanation:
x-7=-5x-1
x-(-5x)-7=-1
x+5x-7=-1
6x-7=-1
6x=-1+7
6x=6
x=6/6
x=1
Answer:
15
Step-by-step explanation:
1 turns in to 3 and you multiply that by 5
Answer:
4 (2 a + 3 b)
Step-by-step explanation:
Simplify the following:
8 a + 12 b
Factor 4 out of 8 a + 12 b:
Answer: 4 (2 a + 3 b)