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3 years ago

6

Tony Michael budgeted $4,550 to buy a used car for his son, Trey. He spent $6,788. How much more or less is the amount spent tha

n the amount budgeted?

1 answer:

Irina18 [472]3 years ago

8 0

Tony spent an extra $2238 than originally planned. That is the case because 6788-4550 equals 2238

2238 more was budgeted

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5+1+(-3)+...+(-395)=

sleet_krkn [62]

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4 years ago

3x+(24x+8)what is the answer

Keith_Richards [23]

We can get rid of the parentheses so it looks like this:

3x + 24x + 8.

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$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

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where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
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The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
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When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

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Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

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Answer:

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Step-by-step explanation:

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