Janet wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed s
2 answers:
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Answer:
can not be expressed as a square of any other number.
Step-by-step explanation:
The number 1953125 is equal to .
Now, the above statement gives an idea that 1953125 i.e. is not a square number as 9 is not a multiple of 2.
So, we can not express as a square of any other number.
We can only express as
.
( Answer )
(a) Take the Laplace transform of both sides:
where the transform of comes from
This yields the linear ODE,
Divides both sides by :
Find the integrating factor:
Multiply both sides of the ODE by :
The left side condenses into the derivative of a product:
Integrate both sides and solve for :
(b) Taking the inverse transform of both sides gives
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that is one solution to the original ODE.
Substitute these into the ODE to see everything checks out: