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3 years ago

Are any of the places shown in the table closer than 1/2 mile to school?

Mathematics

2 answers:

lara [203]3 years ago

4 0

One of them are because the post office is the same length but the rest no

allochka39001 [22]3 years ago

3 0

One is but the post office is the same distance

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What is the slope of the line?<br> y=54x−13π

Grace [21]

If the equation is in the form of y = mx + C, where m and C are real numbers, the slope (which means gradient) of the line is the coefficient of x (I.e. the number to the left of x in simple language), which is m.

In this case, m = 54 and C = -13pie. Both are real numbers, which means that this equation satisfies the form of y = mx + C

m is the coefficient of x, which is 54. 54 is the gradient of this line, which means that for every 54 y-axis units the line increases, the line increases 1 x-axis unit.

Hope this helps! :)

4 0

3 years ago

Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

Find the area of the composite figure to the nearest hundredth.

Lyrx [107]

Answer:

745.31

Step-by-step explanation:

1. 12.5^2 * 2 = 312.5

2. (3,14 * 156,25)/2 = 245.31

3. (30 * 12.5)/2 = 187.5

4. 187.5 + 245.31 + 312.5 = 745.31

4 0

3 years ago

Twice a number (z) added to 21 is equal to 9 times the number added to 7. What is the number?

pickupchik [31]

Answer:

The number is 2

Step-by-step explanation:

Twice a number (z) = 2*z = 2z

Twice a number (z) added to 21 = 2z + 21

9 times the number added to 7 = 9z + 7

9z + 7 = 2z + 21

Subtract 2z form both sides

9z - 2z + 7 = 21

7z + 7 = 21

Subtract 7 from both sides

7z = 21 - 7

7z = 14

Divide both sides by 7

z = 14/7

z = 2

5 0

2 years ago

What is the area of the triangle?

Luda [366]

Answer:

270cm^2

Step-by-step explanation:

The side length is irrelevant and does not matter.

The area of a triangle is found by multiplying the base by the height and then dividing that by two.

For this problem it would be...

30*18=540

540/2=270

So the area would be 270cm^2

3 0

3 years ago