What angle is subtended at the center of a circle of radius 2 km by an arc of length 9 m?

Damion Hardin
2022-05-07
Answered

What angle is subtended at the center of a circle of radius 2 km by an arc of length 9 m?

You can still ask an expert for help

taweirrvb

Answered 2022-05-08
Author has **19** answers

For any circle:

$arc=radius\ast \theta $

Where theta is in radian.

From the given data:

$\theta =arc/radius=0.009/2=0.0045radians$

$arc=radius\ast \theta $

Where theta is in radian.

From the given data:

$\theta =arc/radius=0.009/2=0.0045radians$

generiranfi7qu

Answered 2022-05-09
Author has **1** answers

Recall that the length of an arc of a circle and the corresponding angle subtended at the centre are proportional.

asked 2022-04-06

Suppose I'm given two points: $({x}_{1},{y}_{1})$ and $({x}_{2},{y}_{2})$ (which are real numbers) lying on the circumference of a circle with radius r and centred at the origin, how do I find the arc length between those two points (the arc with shorter length)?

asked 2022-05-01

How to find the center of a circle with given an arbitrary arc. we only have the arc nothing else. Is there any known equation or way to complete the circle.

asked 2022-04-30

If the arc length and chord length between two points (two points on a circle that constitute a minor arc ) in a circle are known , find radius of the circle?

asked 2022-05-03

Let

$f(z)={\displaystyle \frac{z(z-a)}{(z-b)(z-c)(z-d)}}$

be a complex rational function and let $S=\{z\in \mathbb{C}:|z|=1\}$ be the unit circle.

My question:

For which (non-zero complex numbers) $a,b,c$ and $d$ there exist an arc $C$ of $S$ such that $f(C)\subseteq S$ ?

$f(z)={\displaystyle \frac{z(z-a)}{(z-b)(z-c)(z-d)}}$

be a complex rational function and let $S=\{z\in \mathbb{C}:|z|=1\}$ be the unit circle.

My question:

For which (non-zero complex numbers) $a,b,c$ and $d$ there exist an arc $C$ of $S$ such that $f(C)\subseteq S$ ?

asked 2022-05-07

I am attempting to determine the locus of z for $\mathrm{arg}({z}^{2}+1)$. I do know that since ${z}^{2}+1=(z+i)(z-i)$, I could write $\mathrm{arg}({z}^{2}+1)=\mathrm{arg}(z+i)+\mathrm{arg}(z-i)$ but I don’t really know how to figure out the locus of the points from here. How should I approach this? Is there a relationship with the difference in two arguments (arc of a circle)? Thank you!

asked 2022-05-09

Let $n$ points be placed uniformly at random on the boundary of a circle of circumference 1.

These $n$ points divide the circle into $n$ arcs.

Let ${Z}_{i}$ for $1\le i\le n$ be the length of these arcs in some arbitrary order, and let $X$ be the number of ${Z}_{i}$ that are at least $\frac{1}{n}$.

What is $E[X]$ and $Var[X]$?

Any hints will be appreciated. Thanks..

(By the way this problem is exercise 8.12 from the book 'Probability and Computing' by Mitzenmacher and Upfal)

These $n$ points divide the circle into $n$ arcs.

Let ${Z}_{i}$ for $1\le i\le n$ be the length of these arcs in some arbitrary order, and let $X$ be the number of ${Z}_{i}$ that are at least $\frac{1}{n}$.

What is $E[X]$ and $Var[X]$?

Any hints will be appreciated. Thanks..

(By the way this problem is exercise 8.12 from the book 'Probability and Computing' by Mitzenmacher and Upfal)

asked 2022-04-06

It is not possible for a part of any of three conic sections to be an arc of a circle.

It is asked to prove this theorem without using any notation or any modern form of symbolism whatsoever (algebra). But, to me, this seems to be quite a difficult task. How can this be done?

It is asked to prove this theorem without using any notation or any modern form of symbolism whatsoever (algebra). But, to me, this seems to be quite a difficult task. How can this be done?