Find the general solution of the given system. dx dt = 8x − y dy dt = 5x + 4y x(t), y(t) =

The general solution of given system is and .

Step-by-step explanation:

The given differential equations are

      .... (1)

     .... (2)

Differentiate both equations with respect to t.

                      ...... (3)

                   ..... (4)

Using equation (3) and (2).

                  (Using 1)

Using Quadratic formula

If , then

Therefore x(t) is defined as

Using equation (4) and (1).

                    (Using 2)

Using Quadratic formula

Therefore y(t) is defined as

da freeck kinda math is this just drop out

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204