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2 years ago

The equation below describes a circle. x^2+14x+y^2=70. what are the center and radius of the circle?

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

5 0

Answer:

Step-by-step explanation:

center(-7,0)

radius= radical 119

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John spent about 12.5 hours at a water park. He estimated he spent about 30% of the time waiting in line. What would be a reason

Soloha48 [4]

Given:

Total time spent in water park = 12.5 hours

He spent about 30% of the time waiting in line.

To find:

The reasonable amount of time he spent in line.

Solution:

According to the question,

Amount of time he spent in line = 30% of total time

$=\dfrac{30}{100}\times 12.5$

$=0.3\times 12.5$

$=3.75$

Therefore, the reasonable amount of time he spent in line is 3.75 hours.

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2 years ago

Solve 3[-x + (2 x + 1)] = x - 1.

Viktor [21]

The answer is -1. First you distribute the 3. Then u distribute the 3 again to the parentheses. Then solve it from there

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3 years ago

Correct answer gets brainliest

rosijanka [135]

Answer:

yea its 828

Step-by-step explanation:

Its alotta work that ion wanna type but that should b the answer

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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

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

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2 years ago

Factor 18x^3+24x^2-21x-28

maks197457 [2]

Hello my name is Jeff (sorry)

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3 years ago