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

Answer:

Step-by-step explanation:
Given
Points: (1, 9) and (9, 3)
Ratio = 2/3
Required
Determine the coordinate of the center
Represent the ratio as ratio

The new coordinate can be calculated using

Where



Substitute these values in the equation above



Hence;
<em>The coordinates of the new center is </em>
<em></em>
Answer: 12/60 as a percentage is 20%
Step-by-step explanation: boby is 12 and his grandfather is 60 so Bobby’s age is 12/60 of his grandfather and as a percentage it’s 20%
Look at the picture..............
Answer:
Sam gets £30 and Bethan gets £24.
Why?
When dealing with ratios, add up the numbers in the ratio.
5 + 4 = 9
Now, divide the total amount of money by that number.
£54/9 = 6
Now you have the base rate. Multiply each quantity in the ratio by this number.
5*6 = 30
4*6 = 24
Now, the ratio is (in euro) 30:24. This means that Sam has £30 and Bethan has £24.
Check:
30 + 24 = 54