: Show that the solution of the differential equation: = − − − − − is of the form: + + ( − ) = + , When = and =

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that

When

and  

We have:

Rewrite as:

Factorize

Rewrite as:

Factor out 1 + x

Multiply both sides by

Integrate both sides

Rewrite as:

Integrate the left-hand side

Integrate the right-hand side

implies that:

So:

becomes

This gives:

The equation becomes

Take tan of both sides

--- Proved

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:

$15.40 per mile

step-by-step explanation:

you have to round up to 4 because 6 is over 5 so you have to round the 3 up to 4