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2 years ago

HELPPPPPPPPPPPP PLEASEEEE?

Mathematics

1 answer:

Neporo4naja [7]2 years ago

5 0

Answer: V≈56.55

Step-by-step explanation:

V=πr2h

3 = radius

2=height

Fill in the formula = V=πr2h=π·32·2≈56.54867

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Natalia has $54. She earns some money. She spends $37. Natalia ha 62 left. how much did she earn

Leni [432]

Answer:

54-37=17

then

62-17= 45

Therefore, Natalia earned $45.

5 0

2 years ago

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

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

3 0

3 years ago

In a school 40% are boys and 900 are girls. find the total number of students of the school and the number of boys

My name is Ann [436]

Answer:

1500 students

600 boys

Step-by-step explanation:

40% are boys, so 60% are girls.

Writing a proportion:

900 / 60% = x / 100%

x = 1500

There are 1500 students in the school, which means there are 600 boys in the school.

6 0

3 years ago

John bought an old motor bike for $ 5675 and spent $ 453 on its repair. Then he sold it in $ 7265, find out the profit he made.

drek231 [11]

Answer:

1137

Step-by-step explanation:

5675+453

6128

Now

7265-6128

1137

4 0

3 years ago

What is the value of the expression below when w = 5?<br> 2w2 – 2w + 3

bagirrra123 [75]

Answer:

I got you

Step-by-step explanation:

2 time 5 times 2 is 20. This minus 2 times 5 is 10 plus 3 is 13.

5 0

3 years ago