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irakobra [83]
3 years ago
15

to determine the number of trout in a lake a lake a conservationist catches 124 trout tag them and throws them back into the lak

e later 44 trout are called 11 of them are tagged how many trout would the conservationist expect to be in the lake
Mathematics
1 answer:
natali 33 [55]3 years ago
8 0

Answer: 25

Step-by-step explanation:

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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions
monitta
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take z=y', so that z'=y'' and we're left with the ODE linear in z:

y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2

Now suppose y has a power series expansion

y=\displaystyle\sum_{n\ge0}a_nx^n
\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}
\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}

Then the ODE can be written as

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0

\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0

All the coefficients of the series vanish, and setting x=0 in the power series forms for y and y' tell us that y(0)=a_0 and y'(0)=a_1, so we get the recurrence

\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}

We can solve explicitly for a_n quite easily:

a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}

and so on. Continuing in this way we end up with

a_n=\dfrac{a_1}{n!}

so that the solution to the ODE is

y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x

We also require the solution to satisfy y(0)=a_0, which we can do easily by adding and subtracting a constant as needed:

y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}
4 0
3 years ago
What is the value of x?​
Assoli18 [71]
It’s 35 degrees since you do 180-125 to get 35. :)
5 0
3 years ago
Equations
sergij07 [2.7K]

Answer:

2x+12=24

first you subtract 12 from both sides

2x+12=24

-12. -12

The 12-12 should cancel itself, the rest of the equation you bring down to get

2x=12 (because 24-12=12)


Now you have 2x=12.
you then divide 2x by both sides.

2x=12

/2x=/2x

The 2x/2x cancels itself out so you then solve for 12/2x.

For this you just divide 12/2 which is 6!

x= 6 is your final answer.
to check this equation you can plug your number back into x to see if it is true! 2(6)+12=24.
6 times 2 is 12 and 12+12 is 24 so your answer (6) is true!


hope this helps! :D

4 0
2 years ago
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The maximum number of students in a classroom is 26. if there are 16 students sign up for the art class,how many more students c
Marizza181 [45]
Maximum 12 fr longgg
5 0
2 years ago
Read 2 more answers
What is a equivalent expression for -3(7+5g)
bogdanovich [222]

Answer:

= -21 - 15g

Step-by-step explanation:

Given that:

= -3(7+5g)

By simplifying

As "-" sign will invert the inner signs:

= -21 - 15g

I hope it will help you!!

6 0
3 years ago
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