2. The picture shows a feeding trough that is shaped like a right prism.
1 answer:
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The given function is
According to this function, the starting height of the rocket is 20 feet because that's the initial condition of the problem stated by the independent term.
Additionally, we find the maximum height by calculating the vertex of the function V(h,k).
Where a = -16 and b = 300.
Then, we find k by evaluating the function
Hence, the maximum height is 1426.25 feet.
At last, to know the time need to hit the ground, we just use h=9.375 and we multiply it by 2
Hence, the rocket hits the ground after 18.75 seconds.
The characteristic solution follows from solving the characteristic equation,
so that
A guess for the particular solution may be
, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
is already accounted for within 
.
so that
A guess for the particular solution may be
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form