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3 years ago

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a basketball hoop in front of samantha's house is 4 2/3 feet shirter than her house. the height of samantha house is 20 1/6 feet

. what is the height of the basketball hoop?

1 answer:

bekas [8.4K]3 years ago

5 0

Answer:

16 and 1/3

Step-by-step explanation:

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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

IF YOU ANSWER THIS I WILL GIVE YOU BRAINLIEST!! 21PTS

vovangra [49]

<span>200 < 225 + 80x < 550

The 200 is the amount the Jenna currently have.
225 + 80x is the amount that Jenna has to pay given x number of hours.
550 is the sum of Jenna's 200 and additional 350 she can get by selling pre-ordered Cds. This is the maximum amount she can pay for the studio rental and sound technicians.

225 + 80x < 550
80x < 550 -225
80x < 325
80x / 80 < 325/80
x < 4.06 or 4 hours

225 + 80x </span>→ 225 + 80(4) = 225 + 320 = 545
<span>
The number of hours for the sound technician will range from 1 hour to 4 hours.

Assuming they will use 6 hours.

225 + 80(6) = 225 + 480 = 705
705 - 550 = 155

Jenna has to raise an additional $155 to pay off the studio rent and 6 hours of sound technicians.

</span>

4 0

3 years ago

A bookstore owner is conducting market research to forecast sales for the coming year. The bookstore is open 360 days a year and

statuscvo [17]

156 dollars because 13 times 12 (months)
equals 156

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2 years ago

Helppppp can someone answer these questions please

Delvig [45]

Answer:

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Step-by-step explanation:

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3 years ago

What does this mean we never went over it..: Find the difference between 827 and 533. * Please tell me. Thank you!

Nostrana [21]

Answer:

294

Step-by-step explanation:

Difference means subtraction, so you just subtract 533 from 827.

827-533=294

hope this helps! : )

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3 years ago

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