"A small town that encompasses 12 square miles has 3,000 residents. What is the population density of the small town in people p
2 answers:
Answer:
250 people per mile.
Step-by-step explanation:
We need to find the population density. To calculate the population density we need to divide the number of people in the place by the area of the place, that is
puplation density = number of residents / area of the territory. Then,
population density =
Then, the density is 250 people per mile.
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Answer:
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Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:
- A general solution to the above ODE is also given as:
- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.
- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:
- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as: