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9. (a) х = 0 Dit is ook ‘n aanvaarbare antwoord.

(b) 2 х + 6 = 2 х + 6

2 х – 2 х = 6 – 6

0 = 0

  • Hierdie oplossing gee nie ‘n enkele waarde vir х nie.
  • Maar die stelling is waar: Nul is gelyk aan nul.
  • As ons ‘n antwoord kry wat ooglopend waar is, soos 12 = 12 of –3 = –3, ens., dan weet ons dat enige waarde van die veranderlike die vergelyking waar sal maak.
  • Ons gee dus die antwoord: х kan enige waarde aanneem .

(c) 3 – 2 х = –2 – 2 х

–2 х + 2 х = –2 – 3

0 = –5

  • Hierdie antwoord gee nie ‘n waarde vir х nie.
  • Inderwaarheid is die stelling onwaar. Nul is nie gelyk aan negatief vyf nie.
  • As ons ‘n onwaar antwoord kry, soos 5 = –5 of 2 = –9, ens., dan weet ons dat geen waarde van die veranderlike die vergelyking waar sal maak nie.
  • Dus is die antwoord: Daar is geen oplossing nie .

Van nou af moet jy jou oë oophou vir hierdie spesiale gevalle (jy sal hulle nie veel sien nie) en ‘n geskikte antwoord gee

Aktiwiteit 3

Om te bevestig dat oplossings korrek is

[lu 2.4, 2.6]

  • In Wiskunde is dit dikwels moeilik om seker te wees dat jou antwoord korrek is, maar wanneer ons vergelykings oplos, is dit baie maklik: ons kontroleer net ons antwoorde! Dit moet egter baie noukeurig op ‘n spesifieke manier gedoen word.

Dis hoe: Ons kyk weer na vraag 8 hierbo.

(a) 5( х + 1) = 20 gee die oplossing: х = 3

Begin met die oorspronklike vergelyking.

Kontroleer die linkerkant (LK) en regterkant (RK) apart .

Substitueer die oplossing vir х en vereenvoudig:

LK = 5( х + 1) = 5[( 3 ) + 1] = 5(3 + 1) = 5(4) = 20

Soos gewoonlik by substitusie is hakies baie handig.

RK = 20

Omdat die RK en die LK gelyk is, weet ons die oplossing is korrek.

(b) 8 + 4( х – 1) = 0 Veronderstel ons antwoord was х = 2. Toets die antwoord:

LK = 8 + 4( х – 1) = 8 + 4[( 2 ) – 1] = 8 + 4(2 – 1) = 8 + 4(1) = 8 + 4 = 12

RK = 0

Omdat LK ≠ RK weet ons dat 2 nie ‘n oplossing vir die vergelyking is nie.

Natuurlik is die regte antwoord: х = –1. Gaan dit na:

LK = 8 + 4( х – 1) = 8 + 4[( –1 ) – 1] = 8 + 4(–1 – 1) = 8 + 4(–2) = 8 – 8 = 0

LK = RK, en ons het bevestig dat х = –1 die korrekte oplossing is.

(c) х ( х + 3) = х 2 + 6 oplossing: х = 2

LK = х ( х + 3) = ( 2 )(( 2 ) + 3) = 2(2 + 3) = 2(5) = 10

RK = х 2 + 6 = ( 2 ) 2 + 6 = 4 + 6 = 10

LK = RK, dus is х = 2 die korrekte oplossing.

(d) ½ (4 х + 6) = 1 oplossing: х = –1

LK = ½ (4 х + 6) = ½ (4( –1 ) + 6) = ½ (–4 + 6) = ½ (2) = 1

RK = 1

LK = RK, dus is х = –1 die korrekte oplossing.

Gaan nou terug na 5, 6 en 7 en kontroleer jou oplossing op dieselfde manier.

As ons terug gaan na die spesiale gevalle in 9, kan ons hulle ook kontroleer:

(a) 2( х + 1) = х + 2 gee die oplossing: х = 0

LK = 2( х + 1) = 2(( 0 ) + 1) = 2(0 + 1) = 2(1) = 2

RK = х + 2 = ( 0 ) + 2 = 2

LK = RK, dus is х = 0 die korrekte oplossing.

(b) 2( х + 3) = 2 х + 6 Enige getal is ‘n oplossing! Toets bv. 5; of enige ander getal.

LK = 2( х + 3) = 2(( 5 ) + 3) = 2(5 + 3) = 2(8) = 16

RK = 2 х + 6 = 2( 5 ) + 6 = 10 + 6 = 16

LK = RK as х = 5. Inderdaad, LK sal gelyk wees aan RK vir enige waarde.

(c) 3 – 2 х = –2(1 + х ) Daar is geen oplossing nie; probeer 12. Jy kan ander getalle probeer.

LK = 3 – 2 х = 3 – 2( 12 ) = 3 – 24 = – 21

RK = –2(1 + х ) = –2(1 + ( 12 )) = –2(1 + 12) = –2(13) = –26

LK ≠ RK en hulle sal ongelyk wees vir enige getal.

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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it is a goid question and i want to know the answer as well
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characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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Do you know which machine is used to that process?
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how to fabricate graphene ink ?
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for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
Porter
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what is the function of carbon nanotubes?
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I'm interested in nanotube
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what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
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silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
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Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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