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4 years ago

Solve for w. 7w-36 = -2(w-9)

Mathematics

2 answers:

valentina_108 [34]4 years ago

6 0

Answer:

The answer to the question is W=6

iren [92.7K]4 years ago

3 0

Answer:

w= 6

7w-36= -2(w-9)

7w-36= -2w+18 Multiply Parenthesis by -2

7w+2w= 18+36 Move Terms

9w= 54 Collect like terms

/9 . /9

w= 6

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What is a volume, and how is it measured?

dangina [55]

Volume is length x width x height. It measures how much space it can hold inside of a shape.

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3 years ago

Solve using Fourier series.

Olin [163]

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

$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L$
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where the coefficients are obtained by computing

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You should end up with

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(both due to the fact that $f(x)$ is odd)
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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.

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Solve:

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Now multiply it by 1.

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