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3 years ago

How many gallons of gas will she need to purchase

Mathematics

1 answer:

melomori [17]3 years ago

8 0

Plug the 195 into the equation (d)
g = $\frac{195(2)}{26}$
195 x 2 = 390
$\frac{390}{26} = 15$
g = 15
She will need to purchase 15 gallons of gas.

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alex41 [277]

Step-by-step explanation:

there 5^(n+1) + 5^(n+2) = 5^n x 5^1 + 5^n x 5^2 breaking them as x^(a+b) = x^a x x^b

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3 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

One angle of a right triangle measures 78°. What is the measure of the other acute angle?

muminat

Answer:

12°

Step-by-step explanation:

a right triangle implies there is an angle that is 90°

another angle is 78°

the third angle is 180 - (90 + 78) = 180 - 168 = 12°

6 0

3 years ago

Factor completely. 3x^2 + 30x + 75 =?

vladimir1956 [14]

Answer:

the answerrrrrrrrrrr is 3(x+5)^2

3 0

2 years ago

Read 2 more answers

If a plane can travel 490 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the wind and

zavuch27 [327]

let the speed of plane in still air be x and that wind be y

therefore:

x+y=490

x-y=390

next we solve for the values of x and y, first we add the above equations. This will give us:

2x=880

x=880/2

x=440 miles per hour.

substituting the value of x in one of the equations and solving for y we get:

440+y=490

y=490-440

y=50 miles per hour

7 0

3 years ago