Match 1234 to abcd

5 4 3 2 1 0 -2 -1 0 1 5 -2 b = m = Inequality =

kap26 [50]

Answer:

Step-by-step explanation:

5

4

3

2

1

0

-2 -1 0 1

5

-2

b =

m =

Inequality = 5.0?

6 0

3 years ago

Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500500500 leaves

VARVARA [1.3K]

Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500 leaves. each year thereafter, the number of leaves was 40% more than the year before. let f(n) be the number of leaves on the tree in Mohamed's backyard in the n^th year since he started tracking it. f is a sequence. what kind of sequence is it?

Number of leaves on the tree in first year = 500

The number of leaves was 40% more than the year before.

So rate of increase is 40/100 = 0.4

We use exponential growth formula,

f(n) = a(1+r)^n

Where a is the initial number, r is the rate of growth, n is the number of years

We know a= 500, r= 0.4

f(n) = 500(1+0.4)^n

f(n) = 500(1.4)^n

Plug in n=1,2,3...

f(1) = 500

f(2) = 500 * 1.4^1

f(3) = 500 * 1.4^2 and so on

From this we can see that the common ratio is 1.4

Hence it is a Geometric sequence.

8 0

3 years ago

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I need help plez and thanks

Brilliant_brown [7]

He has a total of $58.19.
1 day = $2.74

58.19/2.74
21.24

You can't have 21.2 days, so you need to round down to 21.

Jim can buy lunch for 21 days before he runs out of money on his account.

3 0

3 years ago

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What is the volume? __ cubic inches

ozzi

the answer is 250 cubic inches

3 0

3 years ago

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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