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dezoksy [38]
3 years ago
12

Find the vector equation for the line of intersection of the planes 5x+3y−2z=−45x+3y−2z=−4 and 5x+5z=0

Mathematics
1 answer:
olga_2 [115]3 years ago
8 0

5x+5z=0\implies x+z=0\implies z=-x


5x+3y-2z=7x+3y-2x-2z=7x+3y-2=-4\implies7x+3y=-2


Letting x=t and z=-t, we have


7t+3y=-2\implies y=-\dfrac73t-\dfrac23


so the intersection is given by


\mathbf r(t)=\left(t,-\dfrac73t-\dfrac23,-t\right)

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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
Graph the line, two points to graph Y=4/3x-y
defon
I hope this helps u
And others if ur searching for

4 0
3 years ago
Sushil was thinking of a number. Sushil divides by 7 then adds 7 to get an answer of 12. Form an equation
VikaD [51]

Answer:

The number is 35.

35 divided by 7 is 5, and 5 plus 7 is 12.

:)

3 0
2 years ago
Read 2 more answers
Please I need help asap
jasenka [17]

Answer:

Option D - x = 3 3/5

Step-by-step explanation:

Lets make the left side into an improper fraction :

2 2/5 = 12/5

Now let's make both fraction into equivalent ones but with the same denominator :

2/3 = 10/15

12/5 = 36/15

Now we substitute the equivalent values back into the equation :

10/15 × x = 36/15

Now we multiply both sides by 15 to remove the denominators:

10 × x = 36

Now we divide both sides by 10 and simplify :

x = 36/10

x = 18/5

x = 3 3/5

So our answer will be Option D  

Hope this helped and brainliest please

7 0
2 years ago
Solve inverse operation of A - 5/6 = - 3 2/3
gayaneshka [121]

Answer:

- 2 5/6 = A

Step-by-step explanation:

- 3 2/3 + 5/6 = A

- 2 5/6 = A

3 0
3 years ago
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