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4 years ago

9

Aldo deposits $6000 into an account that pays simple interest at a rate of 4% per year. how much interest will he be paid in the

first 2 years

1 answer:

beks73 [17]4 years ago

3 0

I = P x R x T
I = 6000 x .04 x 2
I = $480

He will be paid $480 interest in the first two years

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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

Find the reciprocal of 3/5

Kisachek [45]

The reciprocal of 3/5 is 5/3.

To get the reciprocal of a fraction, just turn it upside down.

A fraction has a numerator, top number, and a denominator, bottom number.
To get the reciprocal of a fraction, just swap over the numerator and denominator.

If whole numbers, to get the reciprocal of whole number, just divide the whole number by 1 to make it into a fraction, then get the reciprocal of that fraction.

8 0

4 years ago

Read 2 more answers

If the radius of a half-circle is 11...

Xelga [282]

By giving just the radius and asking for the arc length of that circle your answer will be without math is 22
π
feet

But;

Let’s do same math!

Arc length = (()/360)⋅2⋅⋅
(
(
a
n
g
l
e
o
f
a
r
c
)
/
360
)
⋅
2
⋅
π
⋅
r

In this case angle of arc was not specified so: 360∘
∘
was used.

Arc length = ((360)/360)⋅2⋅⋅11
(
(
360
)
/
360
)
⋅
2
⋅
π
⋅
11

Arc length = 22
π
feet

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3 years ago

Express 2 1/2kg as grams

enyata [817]

The answer is 2 1/2kg = <span>2500 g</span>

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3 years ago

The value of (2+3)(2-3) is

NARA [144]

Step-by-step explanation:

(2+3)(2-3)

=5×(-1)

= -5

good morning

have a great day

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3 years ago

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