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1 year ago

8^x=2 what is the value of x

Mathematics

1 answer:

Nadya [2.5K]1 year ago

8 0

Answer:

x = 1/3 or 0.333

Step-by-step explanation:

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What is 62 ÷ 3186 I need to know?

topjm [15]

Answer:

0.02

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

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

2 years ago

A disc has a diameter of 21 cm while a mini disc has a diameter of 14cm. Write the ratio of the mini disc diameter to the disc d

Serjik [45]

Answer:

mini disc diameter:disc diameter

14cm:21cm = 7:10.5 = 3.5:5.25 = 1:1.5

4 0

2 years ago

If you are a student with no assets of any value and have liability insurance on an old car that pays a maximum of $50,000 per a

svetoff [14.1K]

Answer:

Step-by-step explanation:

they will sue for the rest of the money, because they are entitled to it if you are the cause of an accident.

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3 years ago

jen picked 3/4 of a gallon of strawberries in a half of hour .if she keeps picking strawberries at the same rate.how many gallon

ivolga24 [154]

3 gallons of strawberries.

3/4 * 4/1 = 12/4 = 3

or you can use the butterfly method on the fours and get

3/1 * 1/1 = 3

5 0

2 years ago