This equals 0.146341463414634
The answer is (7, -26) for The second endpoint.
We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.
(Ux + Vx)/2 = Mx
(Vx + 3)/2 = 5
Vx + 3 = 10
Vx = 7
And now we do the same thing for y values
(Uy + Vy)/2 = My
(Vy + 6)/2 = -10
Vy + 6 = -20
Vy = -26
This gives us the final point of (7, -26)

Divide both sides by
to get


Substitute
, so that
. Then



The remaining ODE is separable. Separating the variables gives

Integrate both sides. On the left, split up the integrand into partial fractions.




Then

On the right, we have

Solving for
explicitly is unlikely to succeed, so we leave the solution in implicit form,

and finally solve in terms of
by replacing
:



Answer:
2.777777 and -7/3
Step-by-step explanation:
2.7182818459 cannot be written in fraction form therefore it is irrational.
2.777777 is rational because it can be written as the fraction 25/9
The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.
-7/3 is rational because it is already in fraction form.