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2 years ago

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a The function f(x) = |x - 3| can be used to determine how far a number is away from the number 3 on the number line. Find and i

nterpret the given function values and determine an appropriate domain for the function.

1 answer:

jasenka [17]2 years ago

7 0

Answer:

Please add the given function values. Or add an image.

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

2 years ago

Please help me with 9 I really need it

MissTica

Answer:

605 boys

Step-by-step explanation:

If the ratio of boys to girls is 5:7

and there are 847 girls

we can plug this value into the ratio by doing something like:

5:7

= 5/7

= x/847

Because the ratio has to be the same, we can substitute x for the number of boys and solve by the cross method or whatever you guys call it.

5 x

--- x ------

7 847

The x in the middle is just to show the direction you are multiplying.

the 5 is multiplied by the 847 and the 7 is multiplied by x.

847 * 5 = 4,235

4,235 divided by 7 is 605

605 is your answer.

The cross method can be used in most situations.

* is used to represent multiplication btw

4 0

2 years ago

4(-2d-3)=12, someone please solve this for me asap

wlad13 [49]

4(-3 + -2d) = 12

(-3 * 4 + -2d * 4) = 12

(-12 + -8d) = 12

-12 + -8d = 12

-12 + 12 + -8d = 12 + 12

-12 + 12 = 0

0 + -8d = 12 + 12

-8d = 12 + 12

12 + 12 = 24

-8d = 24

d = -3

5 0

2 years ago

A single, six-sided die is rolled. Find the probability of rolling an even number or a number less than 5.

Svetach [21]

The probability of rolling an odd number or a number less than 5 is 5/6.

Probability is the likelihood of the occurrence of an event. It is the ratio of number of events to number of possible outcomes.

The possible outcome from rolling a six-sided die is 1, 2, 3, 4, 5 and 6

P(odd number) = 3/6; P(less than 5) = 4/6; P(odd number and less than 5) = 2/6

Hence:

P(odd number or less than 5) = 3/6 + 4/6 - 2/6 = 5/6

The probability of rolling an odd number or a number less than 5 is 5/6.

8 0

1 year ago

Position vs time for two runners<br><br> Runner a and runner b

Anna35 [415]

Answer:

i8765

Step-by-step explanation:

5 0

2 years ago