We want a solution in the form
with derivatives
Substituting and its derivatives into the ODE,
gives
Shift the index on the second sum to have it start at :
and take the first term out of the other two sums. Then we can consolidate the sums into one that starts at :
and so the coefficients in the series solution are given by the recurrence,
or more simply, for ,
Note the dependency between every other coefficient. Consider the two cases,
- If , where is an integer, then
and so on, with the general pattern
- If , then
and we would see that for all .
So we have
so that one solution is
and the other is
I've attached a plot of the exact and series solutions below with , , and to demonstrate that the series solution converges to the exact one.
Answer:
The answer is letter A, It will continue to get darker.
Explanation:
Adaptive Evolution is a process on how a population inherits traits in the future. This includes <em>natural selection, directional selection, sexual selection, diversifying selection, etc.</em>
Directional Selection- this happens when a particular population of an organism selects for specific phenotypes in order to adapt to its changing environment.
In the case of the<em> Peppered Moth</em>, it's change in color from light to dark is caused by the air pollution that occurred during the Industrial Revolution in England. <em>It changed its color in order to adapt to the dirt or soot that settled in the environment. </em>Peppered moths were originally white in color. This allowed them to camouflage in their clean environment.
If the directional selection continues, that would mean the Peppered Moth will continue to get darker. <u>The thicker the air pollution, the darker it will be.</u> If the air pollution will be lessened, then it will become lighter again.
Answer:
The total cost = $1,099
It would take 100 days
Step-by-step explanation:
Let
x = number of days
Cost of BT&T Cellular = 899 + 2x
Cost of Revizon Electronics = 799 + 3x
Equate the cost of both cell phone services.
899 + 2x = 799 + 3x
899 - 799 = 3x - 2x
100 = x
x = number of days = 100 days
Cost of BT&T Cellular = 899 + 2x
= 899 + 2(100)
= 899 + 200
= $1,099
Cost of Revizon Electronics = 799 + 3x
= 799 + 3(100)
= 799 + 300
= $1,099
Not sure but I think
a) 4/6 which is 66.67%
b) 2/6 which is 33.33%
c) 4/6 which is 66.67%
i haven’t even finished high school so please don’t blame me if im wrong I do think that is the answer
Answer:so the answer is 224 dollars
Step-by-step explanation:
30 percent of 320 is about 96 dollars saving