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A satellite is rotating around Earth at 0.25 radians per hour at an altitude of 242 km above Earth. If the radius of Earth is 6378 kilometers, find the linear speed of the satellite in kilometers per hour.

1655 kilometers per hour

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Key equations

arc length s = r θ
area of a sector A = 1 2 θ r 2
angular speed ω = θ t
linear speed v = s t
linear speed related to angular speed v = r ω

Key concepts

  • An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.
  • An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x -axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
  • To draw an angle in standard position, draw the initial side along the positive x -axis and then place the terminal side according to the fraction of a full rotation the angle represents. See [link] .
  • In addition to degrees, the measure of an angle can be described in radians. See [link] .
  • To convert between degrees and radians, use the proportion θ 180 = θ R π . See [link] and [link] .
  • Two angles that have the same terminal side are called coterminal angles.
  • We can find coterminal angles by adding or subtracting 360° or 2 π . See [link] and [link] .
  • Coterminal angles can be found using radians just as they are for degrees. See [link] .
  • The length of a circular arc is a fraction of the circumference of the entire circle. See [link] .
  • The area of sector is a fraction of the area of the entire circle. See [link] .
  • An object moving in a circular path has both linear and angular speed.
  • The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time. See [link] .
  • The linear speed of an object traveling along a circular path is the distance it travels in a unit of time. See [link] .

Section exercises

Verbal

Draw an angle in standard position. Label the vertex, initial side, and terminal side.

Graph of a circle with an angle inscribed, showing the initial side, terminal side, and vertex.
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Explain why there are an infinite number of angles that are coterminal to a certain angle.

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State what a positive or negative angle signifies, and explain how to draw each.

Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

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How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

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Explain the differences between linear speed and angular speed when describing motion along a circular path.

Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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