We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as dx dt = −λ1x dy dt = λ1x − λ2y dz dt = λ2y (which is discussed here) can be solved with no knowledge other than how to solve a single linear first-order equation. Suppose that time is measured in days, that the decay constants are k1 = −λ1 = −0.139629 and k2 = −λ2 = −0.004891, and that x(0) = 20, y(0) = 0, z(0) = 0. Use a graphing utility to obtain the graphs of the solutions x(t), y(t), and z(t) on the same set of coordinate axes.

b) 36

step-by-step explanation:

18 times 2 is 36

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.