Can 7/30 be reduced?

The height of a cone-shaped statue is 9 ft, and the diameter is 4 ft.

bogdanovich [222]

37.7
The formula is V=πr^2*h/3, and since r is 4/2, you multiply it by π and then multiply it h/3, which is 9/3, so ((2*3.14)*3)= 37.7.

5 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs, In the figure, lines H and KL are parallel. TH K E G D Match each ang

xz_007 [3.2K]

The angle relationship and their reasons are:

m∠HED = m∠FEJ ---> Vertical angles theorem

m∠KFE = m∠DEH ---> Alternate interior angles theorem

m∠LFG = m∠DEH ---> Alternate exterior angles theorem

m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem

m∠DEJ = m∠EFL ---> Corresponding interior angles theorem

m∠LFG + m∠GFK = 180 ---> linear pair

The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:

∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are equal based on the vertical angles theorem.

m∠HED = m∠FEJ ---> Vertical angles theorem

∠KFE and ∠FEJ are alternate interior angles, therefore, they are equal based on the alternate interior angles theorem.

m∠KFE = m∠DEH ---> Alternate interior angles theorem

∠LFG and ∠FEJ are alternate exterior angles, therefore, they are equal based on the alternate exterior angles theorem.

m∠LFG = m∠DEH ---> Alternate exterior angles theorem

∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.

m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem

∠DEJ and ∠EFL are corresponding angles, therefore, they are equal based on the corresponding angles theorem.

m∠DEJ = m∠EFL ---> Corresponding interior angles theorem

∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.

m∠LFG + m∠GFK = 180 ---> linear pair

Learn more about angle relationship on:

brainly.com/question/12591450

4 0

2 years ago

The radius of a circle is 10 cm. Find its circumference in terms of pi

sergejj [24]

Answer:

20 pi is the correct answer

5 0

3 years ago

True or false: the standard deviation of a set of data values is never a negative number

Anestetic [448]

True I think !! Not to sure

8 0

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

3 years ago