A swimming pool has a radius of 8 feet and a height of 5 feet. The swimming pool is shaped like a cylinder. What is the volume o
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Answer:
I assume you know Arithmetic Progression .
so, we have to find the first and last 4-digit number divisible by 5
first = 1000 , last = 9990
we have a formula, = a + (n-1)d
here, is the last 4-digit number divisible by 5.
n is the number of 4-digit even numbers divisible by 5
d is the common difference between the numbers, which is 10 in this case
a is the first 4-digit number divisible by 5
9990 = 1000 + (n-1)*10
899 = n-1
n = 900
Hence, there are 900 4-digit even numbers divisible by 5
Note that if 
, then 
, and so we can collapse the system of ODEs into a linear ODE:
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
. Then
and so
Thus the general solution for
is
and you can find the solution
by simply differentiating .
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
and so
Thus the general solution for
and you can find the solution