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2 years ago

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Suhal buys a total of 24 books from a charity shop. Hardbacks cost £2 and paperbacks cost £1.50. He spends £43.50. Let x represe

nt the number of hardbacks. Let y represent the number of paperbacks. How many of each book does Suhal buy?

1 answer:

laiz [17]2 years ago

4 0

Hello, sorry if this seems a bit odd, it’s a common method though. Hope you can understand this. Thanks

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1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

If

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

Is the line of best fit y=-2.9114x+40.7464 or y=-2.9114x+46.5693 ? Please help i’m in a rush!

Colt1911 [192]

Answer:

line of best fit: y = -2.9114x + 46.569

Step-by-step explanation:

Plugging in your table into Excel, it turns out that y = -2.9114x + 46.569 provides a better fit of the data points into the line. Please see the attached image for details.

Hope this helps.

3 0

3 years ago

A jar of salsa costs $0.95. Neha bought 9 jars of salsa. How much did Neha spend in all? <br><br> $

olga2289 [7]

Answer:

$8.55

Step-by-step explanation:

$0.95 x 9 jars = $8.55

For every jar Neha buys, she spends $0.95, and buying 9 jars in total, she pays $8.55 in total.

5 0

3 years ago

Read 2 more answers

What is 2 less than five times a number

miv72 [106K]

Answer:

2<5*X

Step-by-step explanation:

Hope this helped, Have a Wonderful Day!!

8 0

3 years ago

Read 2 more answers

The length of a rectangle is 4 ft longer than its width.

son4ous [18]

Answer:

96

Step-by-step explanation:

40=4x+8

32=4x

x=8

other side x+4 is 12

area is 12×8

96

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3 years ago