All categories

3 years ago

Dai has 3 meters of fabric that he wants to cut into 5 equal-sized pieces.

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

Answer:each piece has 1/5 of 3 meters of fabric.

Step-by-step explanation:

You might be interested in

Solve using Fourier series.

Olin [163]

With $2L=\pi$ , the Fourier series expansion of $f(x)$ is

$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L$
$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos2nx+\sum_{n\ge1}b_n\sin2nx$

where the coefficients are obtained by computing

$\displaystyle a_0=\frac1L\int_0^{2L}f(x)\,\mathrm dx$
$\displaystyle a_0=\frac2\pi\int_0^\pi f(x)\,\mathrm dx$

$\displaystyle a_n=\frac1L\int_0^{2L}f(x)\cos\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle a_n=\frac2\pi\int_0^\pi f(x)\cos2nx\,\mathrm dx$

$\displaystyle b_n=\frac1L\int_0^{2L}f(x)\sin\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle b_n=\frac2\pi\int_0^\pi f(x)\sin2nx\,\mathrm dx$

You should end up with

$a_0=0$
$a_n=0$
(both due to the fact that $f(x)$ is odd)
$b_n=\dfrac1{3n}\left(2-\cos\dfrac{2n\pi}3-\cos\dfrac{4n\pi}3\right)$

Now the problem is that this expansion does not match the given one. As a matter of fact, since $f(x)$ is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.

One possibility is that you're actually supposed to use the even extension of $f(x)$ , which is to say we're actually considering the function

$\varphi(x)=\begin{cases}\frac\pi3&\text{for }|x|\le\frac\pi3\\0&\text{for }\frac\pi3$

and enforcing a period of $2L=2\pi$ . Now, you should find that

$\varphi(x)\sim\dfrac2{\sqrt3}\left(\cos x-\dfrac{\cos5x}5+\dfrac{\cos7x}7-\dfrac{\cos11x}{11}+\cdots\right)$

The value of the sum can then be verified by choosing $x=0$ , which gives

$\varphi(0)=\dfrac\pi3=\dfrac2{\sqrt3}\left(1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots\right)$
$\implies\dfrac\pi{2\sqrt3}=1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots$

as required.

5 0

3 years ago

Ben earns $9 per hour and $6 for each delivery he makes. He wants to make $155 in an 8-hour workday. What is the least number of

ioda

Find how much he will earn
we know he will earn 8 hours sofirst find how many he earns
9 per hour
8 hou
9*8=72
72+6*numberofdeliveries=155
minus 72
6*numberofdeliviers=83
divide by 6
number of delevieries=13.8
he can't make 13.8, round up to get 14

answer is 14 deliveries

7 0

3 years ago

Read 2 more answers

PLEASE HELP! I’M SO CONFUSED!!

romanna [79]

Answer:

The answer is 7.

Step-by-step explanation:

4 divided by 7 is 0.571428 these just keep repeating over and over again so the closest dividable number of 6 (6 is how many digits there are before it repeats) is 1998 so the 2nd digit in .571428 is 7 hope this helps.

8 0

3 years ago

Please help A. 13 B. 26 C. 40 D. 36 D. 41

Morgarella [4.7K]

The value of x is 26.

4 0

3 years ago

Read 2 more answers

7 cards are drawn from a standard deck of 52 playing cards. How many different 7-card hands are possible if the drawing is done

Vladimir [108]

Answer:

The number of different 7 card hands possibility is 133784560

Step-by-step explanation:

The computation of the number of different 7 card hands possibility is shown below:

Here we use the combination as the orders of choosing it is not significant

So,

The number of the different hands possible would be

= $^{52}C_7$

= 52! ÷ (7! × (52 - 7)!)

= 133784560

Hence, the number of different 7 card hands possibility is 133784560

4 0

3 years ago