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3 years ago

In the coordinate plane, what is the length of the line segment that connects points at (0,-1) and (-7, -2)?

Mathematics

1 answer:

notka56 [123]3 years ago

7 0

In the coordinate plane, the length of the line segment that connects points at (0, -1) and (-7, -2) is 7.07 units.

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When will the ball hit the ground

Likurg_2 [28]

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A picture or drawing

Thanks - Madilyn.

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3 years ago

Read 2 more answers

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

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3 years ago

An item costs $330 before tax, and the sales tax is $23.10 . find the sales tax rate. write your answer as a percentage.

ad-work [718]

Divide sales tax amount over the item's cost
23.1 / 330 = 0.07
Therefore the sales tax is 7%

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3 years ago

Maximim height of the diver

Mila [183]

Answer:

Step-by-step explanation:

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2 years ago

Find the value of x and the length of each side

AlladinOne [14]

The 3 sides of the triangle are PR = 8.4, OR = 5.4 and OP = 3.1

Step-by-step explanation:

Step 1 :

Given

PR = 3x - 0.6

OP = x + 0.1

OR = x + 2.4

Also the 2 sides OR and PR are said to be equal.

So we have OR = PR

=> 3x - 0.6 = x + 2.4

=> x = 2.4 + 0.6 => x = 3

Step 2 :

we have ,

PR = 3x - 0.6 = 3(3) - 0.6 = 8.4

OR = x + 2.4 = 3 + 2.4 = 5.4

OP = x + 0.1 = 3 + 0.1 = 3.1

Step 3 :

Answer :

The 3 sides of the triangle are

PR = 8.4

OR = 5.4

OP = 3.1

8 0

3 years ago