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Aktiwiteit 4

Om uitdrukkings en vergelykings te onderskei

[lu 2.1, 2.6]

  • Uitdrukkings is kombinasies van letters ( a , b , х , y , ens.), bewerkings (+, –, ×, ) en getalle (1, –5, π, ½ , ens.), asook hakies en ander tekens. Dit sluit nie gelykaantekens in nie.
  • ‘n Uitdrukking is nogal soos ‘n woord of ‘n frase – dit het nie ‘n werkwoord nie.
  • ‘n Paar voorbeelde: х , х 3 , 5½ , 2πr, 5( ab bc ), 5 a 3 – 3 a 2 + a – 3, 2 a + b size 12{ sqrt {2 left (a+b right )} } {} , 5a 4 2a 2 size 12{ { {5a - 4} over {2a rSup { size 8{2} } } } } {} , ens.
  • ‘n Uitdrukking kan slegs gemanipuleer word, gewoonlik om dit te vereenvoudig. Dit kan nie opgelos word nie; dit het nie ‘n oplossing nie. Jy kan jou werk slegs kontroleer deur agteruit te werk om te sien of jy by die begin uitkom.
  • ‘n Vergelyking is doodgewoon twee uitdrukkings met ‘n gelykaanteken tussenin!
  • Dit is soos ‘n sin met ‘n werkwoord; dit maak ‘n stelling. Byvoorbeeld 2 х – 3 = 45 sê dubbel ‘n sekere getal, met drie verminder, is gelyk aan 45. Dis ons werk om daardie getal te bepaal.
  • Vergelykings word opgelos; hulle het oplossings wat bevestig kan word.
  • Ons vereenvoudig heelwat tydens die oplos van vergelykings, maar ons doen meer – ons word toegelaat om meer te doen. Onthou dat ons terme kan bytel of aftrek, as ons dit net aan beide kante doen! Ons kan met faktore deel of vermenigvuldig, as ons dit net aan beide kante doen. Omdat ‘n uitdrukking nie twee kante het nie, kan ons hierdie bewerkings nie op uitdrukkings toepas nie. Moenie uitdrukkings en vergelykings verwar nie, en oefen totdat jy instinktief weet wat om te doen.

Aktiwiteit 5

Om twee vergelykings gelyktydig op te los

[lu 2.4, 2.9]

1. Die lyn in diagram 1 het definisie-vergelyking y = 2.

Vraag: Lê die punt (1 ; 1) op die lyn?

Antwoord: Ons kan die antwoord grafies (deur die grafiek te bekyk) oplos. Dis duidelik dat die punt nie op die lyn lê nie, en dus is die antwoord nee .

Ons kan die antwoord algebraïes oplos, soos volg: Substitueer die punt (1 ; 1) vir ( х ; y ) in die vergelyking. Doen LK en RK apart soos voorheen.

LK: y = ( 1 ) = 2 RK: 2 LK ≠ RK – die punt (1 ; 1) lê nie op y = 2 nie.

Vraag: Lê die punt (–2 ; 2) op die lyn?

Grafies : Ja.

Algebraïes : LK: y = ( 2 ) = 2 RK: 2 LK = RK; Ja.

Vraag: Lê die punt (1½ ; 2) op die lyn? Bepaal die antwoord beide grafies en algebraïes .

2. Die lyn in diagram 2 word gedefinieer deur die vergelyking y = 2 х – 1.

Vrae: Lê die punt (0 ; 0) op die lyn?

Lê die punt (1 ; 1) op y = 2 х – 1?

Lê die punt (1½ ; 2) op die lyn?

3. In diagram 3 is dieselfde twee lyne saam op een stel asse getrek.

Bepaal grafies: Watter punt lê op beide lyne? Die antwoorde op vrae 1 en 2 hierbo sal help.

Dit is ooglopend uit diagram 3 dat die enigste punt op beide lyne (1½ ; 2) is.

  • So bepaal ons dit algebraïes:

Die vergelyking y = 2 gee y die waarde 2. Substitueer nou hierdie waarde in y = 2 х – 1.

As ons dan die vergelyking oplos, kry ons die waarde van х . So:

Substitueer: ( 2 ) = 2 х – 1 en los op vir х :

2 = 2 х – 1 х - terme na links

–2 х + 2 = –1 konstante terme na regs

–2 х = –2 – 1 vereenvoudig

–2 х = –3 deel beide kante deur –2

х = –3  –2 vereenvoudig

х = 1½

Dit toon die punt waar die lyne mekaar sny: ( х ; y ) = (1½ ; 2).

  • In hierdie metode het ons die twee vergelykings gelyktydig opgelos om die waardes van beide veranderlikes te vind wat beide vergelykings waar maak. As ‘n vergelyking slegs een veranderlike het, benodig ons slegs een vergelyking om daardie waarde van die veranderlike te vind wat die vergelyking waar maak. As ons twee veranderlikes het, benodig ons twee vergelykings om op te los vir die twee veranderlikes.


1 Los algebraïes op vir a en b : 2 a – 3 b = 0 en a = 6

2 Waar sny die lyne y = – х + 5 en y = –1? Bepaal die antwoord algebraïes.

3 Lê die punt (3 ; 4) op beide lyn y = 4 en lyn y = – х + 1? Doen algebraïes.

4 Sny die lyne y = –2 en y = 2? Bepaal die antwoord algebraïes.

Aktiwiteit 6

Om eenvoudige eksponiensiële vergelykings op te los

[lu 2.4, 2.8]

Probleme en sommige antwoorde.

1 Ek dink aan ‘n getal waarvan die kwadraat 100 is. Wat is die getal?

Die getal kan 10 wees, want 10 2 = 100. Maar is –10 nie ook ‘n korrekte antwoord nie?

Ja, hierdie probleem het twee geldige antwoorde!

Maak ‘n vergelyking uit hierdie stelling: Gestel die getal is х .

х 2 = 100

х 2 = 10 2 of х 2 = (–10) 2 Die hakies is noodsaaklik – sien jy dit?

х = 10 of х = –10 Beide antwoorde is geldig.

2 Ek dink aan ‘n negatiewe getal waarvan die kwadraat 25 is. Wat is dit?

Laat die getal y wees

y 2 = 25

y 2 = (5) 2 of y 2 = (–5) 2

y = 5 of y = –5 is die twee oplossings verskaf deur die vergelyking.

Die probleemstelling bevestig egter dat y = –5 die enigste geldige antwoord is.

3 Vind daardie getal wat ‘n derdemag van 27 het.

Laat die getal х wees

х 3 = 27  х 3 = 3 3 х = 3.

Hoekom kan х nie –3 wees nie?

4 Die derdemag van ‘n sekere getal is –8. Wat is die getal?

5 Los op vir х , en bevestig jou antwoord met die LK/RK metode:

a) х 2 = 64

b) х 2 = 36

c) х 2 = –100

d) х 2 – 49 = 0

e) х 2 = 12,25

f) 3 х 2 = 12

g) 2 х 2 – 10,58 = 0

6 Los op vir a en kontroleer jou antwoord:

a) a 3 = 64

b) a 3 + 1 = 0

c) 2 a 2 = 16

d) a 4 = 81

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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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