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
.
Answer:
75/16 or 4 11/16
Step-by-step explanation:
The first answer is an improper fraction, and the second answer is a mixed number...
The answer would be j=61 in order to make the equation true
Part (a)
<h3>Answer: 0.2</h3>
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Work Shown
It costs $15 to rent a bike for 3 hours. We can write the following ratio below
15 dollars : 3 hours
To represent the connection of the two concepts (dollars connecting with hours)
We want the "15 dollars" to turn into "1 dollar". This is because the phrasing "per dollar" really means "per 1 dollar".
Divide both sides of the ratio by 15 to achieve this goal.
15 dollars : 3 hours
15/15 dollars : 3/15 hours
1 dollar : 1/5 hours
1 dollar : 0.2 hours
0.2 hours : 1 dollar
So we get 0.2 hours per dollar.
As a side note, 0.2 hours = 0.2*60 = 12 minutes.
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Part (b)
<h3>Answer: 3.38</h3>
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Work Shown
27 pages : 8 minutes
27/8 pages : 8/8 minutes
3.375 pages : 1 minute
3.38 pages : 1 minute
I'm dividing both parts of the original ratio by 8 to turn "8 minutes" into "1 minute" (due to the phrasing "per minute"). Don't forget to round to 2 decimal places.
Well, from what you’ve posted, it seems that a negative value cannot be accepted since that would imply she has gone underwater. She also cannot go above 300 feet since she is going downwards from a max height.
