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3 years ago

Which polynomial identity will prove that 49 − 4 = 45?

1 answer:

3 0

49 is a square of 7 and 4 is a square of 2. To get 45 you need to subtract 7² and 2². Therefore, its the difference of squares.

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A survey of 160 students is taken to determine whether they play sports and whether they have a job. Of the 71 students who play

Iteru [2.4K]

Answer:

The answer is 44- so B

Step-by-step explanation:

I did the quiz, and that was the correct answer. ( Also I took this on goformative.)

3 0

3 years ago

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

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

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

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

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

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

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

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

3 0

3 years ago

2. A dance floor is a square with an area of 1,444 FT(2). What are the dimensions of the dance floor?

svet-max [94.6K]

Answer:

The answer is C use a calculator

Step-by-step explanation:

not that hard lol

8 0

3 years ago

In AJKL, the measure of ZL=90°, JL = 55, LK = 48, and KJ = 73. What

Juli2301 [7.4K]

Together I think it’s the same way that you can get the one to the one you have on your computer problems you have no proof that I have it on my computer problems I have lost all the same information I I don’t have any proof that you are in my account so so much you have to pay for it and I’m sorry you don’t know where I can get you I know I

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2 years ago

12(5 x-4.5)=36 what is the value of x

-Dominant- [34]

Answer:

3 /2

Step-by-step explanation:

12(5x−4.5)=36

(12)(5x)+(12)(−4.5)=36(Distribute)

60x+−54=36

60x−54=36

Step 2: Add 54 to both sides.

60x−54+54=36+54

60x=90

Step 3: Divide both sides by 60.

60x

90 /60

3 /2

6 0

3 years ago