A number multiplied by 7 is less than 21. Which of the following expressions

Jan needed to empty 18 gallons of water from a tub into jugs that hold 0.5 gallons of water. How many jugs did Jan need?

Ilia_Sergeevich [38]

So you would do,
18 gallons of water divided by 0.5 gallons of water
if you did that correctly you should have gotten... 36 jugs

8 0

2 years ago

The radius of a semicircle is 4 miles. What is the semicircle's area?

adell [148]

Answer:

8 $\pi$ miles or 25.133 miles

Step-by-step explanation:

your radius is 4 miles.

The area of a circle is A= $\pi r^{2}$

Therefore, the area of this circle is $4^{2} \pi$ , or 16 $\pi$

Half of this area, because what you're looking for is a semi-circle, is:

8 $\pi$ (exact) or 25.133 (rounded) miles.

6 0

2 years ago

Use the exponent properties to simplify the following<br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3x%5E3y%5E2z%7D%7B27xy%5E2

7nadin3 [17]

Step-by-step explanation:

x^2/9 z^2

hiiii checkout the steps

7 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

Give B= {a,l,g,e,b,r} and C={m,y,t,h} find B U C

masha68 [24]

The union of a collection of sets is the set of all elements in the collection.

We have B = {a, l, g, e, b, r} and C = {m, y, t, h}

6 0

2 years ago