All categories

3 years ago

Find the length of an arc of 40° in a circle with an 8 inch radius.

Mathematics

1 answer:

gulaghasi [49]3 years ago

6 0

Answer:

5.59 inch

Step-by-step explanation:

Arc Length = 2 * π * 8 * (40/360) = 16π/9 = 5.59

You might be interested in

What is 30% written as a fraction in simplest form? (Lol I asked the wrong question earlier this is what I meant )

igor_vitrenko [27]

Answer:

3/10

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

If i clock out at 11:53 and i have 30 Minutes what time do i get in?

lara [203]

Answer:

you get in at 11:23

Step-by-step explanation:

53-30=30

so 11:23

6 0

3 years ago

Read 2 more answers

The area of a circular sun spot is growing at a rate of 1,200 km2/s.

Tpy6a [65]

A)

$\bf \textit{area of a circle}\\\\
A=\pi r^2
\\\\\\
\cfrac{dA}{dt}=\pi \cdot 2r\cfrac{dr}{dt}\implies \cfrac{dA}{dt}=2\pi r\cfrac{dr}{dt}\implies \cfrac{\frac{dA}{dt}}{2\pi r}=\cfrac{dr}{dt}\\\\
-----------------------------\\\\
\left. \cfrac{dr}{dt} \right|_{r=3000}\implies \cfrac{1200}{2\pi \cdot 3000}=\cfrac{dr}{dt}\\\\$

B)

$\bf A=\pi r^2\qquad A=490000\implies 490000=\pi r^2\implies \sqrt{\cfrac{490000}{\pi }}=r
\\\\\\
\left. \cfrac{dr}{dt} \right|_{r=\sqrt{\frac{490000}{\pi }}}\implies \cfrac{1200}{2\pi \cdot \sqrt{\frac{490000}{\pi }}}=\cfrac{dr}{dt}
$

8 0

3 years ago

Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a po

jeka94

Answer:

Zeroes : 1, 4 and -5.

Potential roots: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

Step-by-step explanation:

The given equation is

$x^3-21x=-20$

It can be written as

$x^3+0x^2-21x+20=0$

Splitting the middle terms, we get

$x^3-x^2+x^2-x-20x+20=0$

$x^2(x-1)+x(x-1)-20(x-1)=0$

$(x-1)(x^2+x-20)=0$

Splitting the middle terms, we get

$(x-1)(x^2+5x-4x-20)=0$

$(x-1)(x(x+5)-4(x+5))=0$

$(x-1)(x+5)(x-4)=0$

Using zero product property, we get

$x-1=0\Rightarrow x=1$

$x-4=0\Rightarrow x=4$

$x+5=0\Rightarrow x=-5$

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

$x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}$

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

3 0

3 years ago

if julie ran 3.6 miles from home to the gym and then walked 0.7 miles to the store she then ran from the store home if her total

o-na [289]

So,

Home ---- gym = 3.6 mi.
gym ---- store = .7 mi.
store ----- home = x

3.6 + .7 + x = 7.2 mi.

Collect Like Terms

4.3 + x = 7.2

Subtract 4.3 from both sides
x = 2.9

The distance from the store to her home is 2.9 miles.

4 0

3 years ago