1. determine the degree of homogeneity of the function s(x,y) = x^2 y + xy^2, and show that euler's theorem holds. 24 zvy

Degree

Step-by-step explanation:

The function that you have is a homogeneous function of degree . In fact, if and we have that:

To verify that the Euler Theorem holds we need to show that:

.

To do that let's compute the partial derivatives:

Then,

The numbers are 18, 13, and 72.

Step-by-step explanation:

Let the three numbers be represented by a, b, and c.

The sum of the three is 103. Thus, we can write that:

The second number is five less than the first. So:

And the third number is four times the first. So:

Substitute:

Solve for a. Combine like terms:

Add five to both sides:

And divide both sides by six. Therefore:

So, the first number is 18.

Since the second number is five less than the first, the second number is 13.

And since the third number is four times the first, the third number is 72.