Write y = 2x + 8 in standard form.

A 96 ounce container of orange juice cost $4.80 at what price should a 128 ounce container be sold in order for the unit rate fo

Alex

It is $0.05 per ounce, so at that rate, a 128 oz container would cost $6.40.

5 0

2 years ago

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Joshua sponsored a fundraiser that 708 people attended. He raised $8,640. He charged $15 for balcony seats and $10 for ground se

lozanna [386]

312 people bought balcony seats and 396 people bought ground seats.

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

2 years ago

The Ferris wheel shown makes 16 revolutions per ride. How far would someone travel during one ride? Round your final answer to t

sertanlavr [38]

Complete question :

The diameter of the ferris Given is 63 feets

Answer:

3165 feets

Step-by-step explanation:

Given that :

Diameter of ferris = 63 feets

Recall :

Circumference of a circle = 2 * pi * Radius

Or

Circumference = pi * d

Hence,

Circumference of wheel = 3.14 * 63 = 197.82 feets

Distance traveled during one ride :

Circumference of wheel * number of revolutions

197.82 * 16 = 3165.12

= 3165 feets (nearest whole number)

4 0

2 years ago

2/3(x+6)=-18 what is the value of x

sladkih [1.3K]

Answer:

x = -33

Step-by-step explanation:

2/3(x+6)=-18

Multiply each side by 3/2

3/2*2/3(x+6)=-18*3/2

x+6 = -27

Subtract 6 from each side

x +6-6 = -27-6

x = -33

4 0

3 years ago

Write y = 2x + 8 in standard form.​

Write y = 2x + 8 in standard form.