A first-order differential equation is represented by the equation $\mathbf{ \dfrac{dy}{dx} =f (x,y) }$ with 2 variables x & y, including its function f(x,y) specified on a xy-plane.

Given that:

$\mathbf{f(x,y) =-22x^2+22xy-11y^2+110x-40y-23}$

Let us first differentiate the above equation with respect to x, we have:

$\mathbf{\dfrac{\partial f(x,y) }{\partial x} = -44x +22y -0+110-0-0=0}$

$\mathbf{\implies -44x +22y+110=0}$ (multiply by -1)

44x - 22y = 110 ------ (equation 1)

Now, differentiating with respect to y, we have:

$\mathbf{\dfrac{\partial f(x,y) }{\partial y} =0 +22x-22y +0-40-0=0}$

$\mathbf{\implies 22x-22y -40=0}$

22x - 22y = 40 ----- (equation 2)

Now, we have a system of equations:

44x - 22y = 110

- ---- ( subtracting equation 2 from 1; elimination method)

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x = 70/22

Replacing the value of x into equation (1), we have:

44x - 22y = 110

44(70/22) - 22y = 110

140 - 22y = 110

140 - 110 = 22y

30 = 22y

y = 30/22

Learn more about the first-order conditions in differential calculus here;

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4 0

2 years ago

Use euler's formula to find the missing number <br><br>vertices: 11<br>edges: 34<br>Faces: ?

larisa [96]

Answer:

F = 25

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2

Here V = 11, E = 34, thus

F + 11 - 34 = 2

F - 23 = 2 ( add 23 to both sides )

F = 25

8 0

3 years ago