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2 years ago

A computer was on sale for 3/4 of the original price. If the original price was $1,600 what was the sale price?

Mathematics

1 answer:

Gre4nikov [31]2 years ago

7 0

Answer:

$1200

Step-by-step explanation:

3/4 of 1600 is 1200

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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]

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

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

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

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3 years ago

Who can help me ????.<br>instruction find the missing length.

djverab [1.8K]

Answer:

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2 years ago

the derivative of the function f is given by f'(x)=x^2cos(x^2). How many points of inflection does the graph of f have on the op

Vsevolod [243]

The point of inflection is calculated by equating the second derivative to zero and determining x from there.

f"(x) = -x²2xsinx² + cosx²(2x) = 0

2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0

2x = 0 ⇒ x = 0
cosx² - xsinx² = 0 ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)

Thus, the function only has 1 point of inflection and it is at x = 0.

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3 years ago

Please help me with this asiment please I’ll do anything!!!!

ozzi

Answer: Line 2

Step-by-step explanation:

Look at the dots on the coordinate grid. The line of fit is a line around those dots, so in this case, the majority of the dots around line 2.

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DUE IN A FEW PLS HELP

BARSIC [14]

Answer:

Step-by-step explanation:

A solid dot means include that number. An open circle means to not include that number.

Let's look at what each choice means.

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