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2 years ago

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What is the slope of the line through (2,-2)(2,−2)(, 2, comma, minus, 2, )and (9,3)(9,3)(, 9, comma, 3, )? Choose 1 answer: Choo

se 1 answer:
a.(Choice A) A \dfrac57 7 5 start fraction, 5, divided by, 7, end fraction
b.(Choice B) B -\dfrac75− 5 7 minus, start fraction, 7, divided by, 5, end fraction
c.(Choice C) C -\dfrac57− 7 5 minus, start fraction, 5, divided by, 7, end fraction
d.(Choice D) D \dfrac75 5 7

1 answer:

svp [43]2 years ago

3 0

Answer:

A) $\frac{5}{7}$

Step-by-step explanation:

Use the two-points formula for the slope of a line.

We know that the points (2,-2) and (9,3) are on the line. If (a,b),(c,d) are points on a line then the slope m is defined by the equation $m=\frac{d-b}{c-a}$ . In this case, a=2,b=-2,c=9 and d=3 then the slope is $m=\frac{3-(-2)}{9-2}=\frac{5}{7}$ .

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2(length + width). What is the perimeter, in units, of a rectangle of length fraction 1 over 3 unit and width fraction 1 over 2

lubasha [3.4K]

Answer:

<u>1 and 2/3</u>

Step-by-step explanation:

If

length = 1/3 and width= 1/2

then the equation will look like this,

2(1/3+1/2)

1/3+1/2= 5/6

2(5/6)=<u> 1 and 2/3</u>

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2 years ago

Which of the following statements is false

Molodets [167]

Answer:

the second one is false

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2 years ago

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Given regular pentagon ABCDE, what are the coordinates of vertex C?

nata0808 [166]

Answer: a

Step-by-step explanation: C is in quadrant 1 and quadrant 1 is (+,+)

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3 years ago

Solve using Fourier series.

Olin [163]

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

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

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

What is the value of x?<br> a) 18°<br> b) 36°<br> c) 43°<br> d) 86°

dmitriy555 [2]

Answer:

I think is 18

Step-by-step explanation:

because is the same of the L

7 0

2 years ago