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2 years ago

Determine the point that lies on the equation y = -5x - 3.

Mathematics

1 answer:

scZoUnD [109]2 years ago

8 0

Answer:

(4, -23)

Step-by-step explanation:

We are given;

The equation, y = -5x -3

We are needed to determine the point that lies on the equation;

We need to know that for a point to be lying on the equation it must satisfy the equation.
This means when we use the value of x in the equation we should get the exact value of y of the given point;

Therefore, in this case;

Point (4, -23)

Replacing x = 4 in the equation;

y = -5(4) - 3

= -23

Therefore, the point lies on the equation as the point satisfies the equation

Thus, the required point is (4, -23)

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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

2 years ago

For which values of x will the rational expression below be undefined? Check

ololo11 [35]

Answer:

-2

Step-by-step explanation:

For the given expression to be undefined, this means that the denominator must be zero.

From the given expression, the denominator is x + 2

Equating this to zero;

x+2 = 0

Subtract 2 from both sides

x+2-2 = 0 -2

x = -2

Hence the value of x that makes it undefined is -2

3 0

2 years ago

What is the value of StartFraction 1.6 times 10 Superscript 14 Baseline Over 3.2 times 10 Superscript 7 Baseline EndFraction in

Lubov Fominskaja [6]

Answer:

C. 5.0*10 superscript 6

Step-by-step explanation:

i just took the test and i got it right.

8 0

2 years ago

In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in

Minchanka [31]

Answer:

Step-by-step explanation:

7 0

2 years ago

Can someone tell me what 8 x 1 1/2 equals

Lady_Fox [76]

8 x 1 = 8
8 x 1/2 = 4
8+4 =12
therefore, 8 x 1 1/2 = 12

7 0

3 years ago

Read 2 more answers