What is the length of a side of a cube with volume 729 cm3?
1 answer:
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Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is:
Answer:
[See Below]
Step-by-step explanation:
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- Rearrange the equation by subtracting what is to the right of the greater than sign (≤, ≥) from both sides of the inequality:
- Pull out like factors:
- Divide both sides by
:
- Remember to flip the inequality sign:
- Subtract
from both sides:
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