From start to finish, a machine can fill a bottle of water, seal it, label it, and pack it in 8.6 seconds. About how many bottle
2 answers:
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The vertices of the triangle are the points where any pair of lines intersect.
We start by setting up the system
Using one of the two equations we can derive the correspondent y value:
So, one vertex is (1, 1)
We choose the other two pairs of lines to find the other vertices:
So, the three vertices are (1, 1), (2, 0), (-1, -3).
a) The solution of this <em>ordinary</em> differential equation is .
b) The integrating factor for the <em>ordinary</em> differential equation is .
The <em>particular</em> solution of the <em>ordinary</em> differential equation is .
<h3>How to solve ordinary differential equations</h3>
a) In this case we need to separate each variable () in each side of the identity:
(1)
Where is the integration constant.
By table of integrals we find the solution for each integral:
If we know that and
<em>, </em>then the integration constant is
.
The solution of this <em>ordinary</em> differential equation is .
b) In this case we need to solve a first order ordinary differential equation of the following form:
(2)
Where:
- Integrating factor
- Particular function
Hence, the ordinary differential equation is equivalent to this form:
(3)
The integrating factor for the <em>ordinary</em> differential equation is .
The solution for (2) is presented below:
(4)
Where is the integration constant.
If we know that and
, then the solution of the ordinary differential equation is:
If we know that and
, then the particular solution is:
The <em>particular</em> solution of the <em>ordinary</em> differential equation is .
To learn more on ordinary differential equations, we kindly invite to check this verified question: brainly.com/question/25731911