Answer: The required solution is
Step-by-step explanation:
We are given to solve the following differential equation :
where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.
From equation (i), we have
Integrating both sides, we get
Also, the conditions are
and
Thus, the required solution is
Given:
The focus of the parabola is at (6,-4).
Directrix at y=-7.
To find:
The equation of the parabola.
Solution:
The general equation of a parabola is:
...(i)
Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.
The focus of the parabola is at (6,-4).
On comparing both sides, we get
...(ii)
Directrix at y=-7. So,
...(iii)
Adding (ii) and (iii), we get
Putting in (ii), we get
Putting in (i), we get
Therefore, the equation of the parabola is .