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2 years ago

Please answer fast!

Mathematics

2 answers:

asambeis [7]2 years ago

7 0

Answer A

In^2 this multiplies the number used by itself therefore in your case 283 x 283. You are using the measurement for inches.

Lorico [155]2 years ago

3 0

Answer: C

Step-by-step explanation:

A says the polygon's measurements are 283 inches by 283 inches. Is it Correct? No. If we multiply these numbers we get 80,089 inches squared, which is not equal to our actual surface of 283 inches squared.

B says the polygon's volume is 283 inches cubed, which is not correct because it says that a certain measurement of a polygon is 283 inches squared, not cubed, which means we got a surface/area, not a volume.

C says that our 283 inches squared area could fit 283 one-inch by one-inch squares, which is correct because one-inch by one-inch is an one inch squared area, if we multiply this one-inch squared by the number 283, we get 283 inch squared area.

And D couldn't be because the answer is C.

Hope I Helped!

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

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$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
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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

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