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Wiskunde

Graad 9

Getalle

Module 3

Waarom is pythagoras so belangrik?

ONDERSOEK

1.1 Werk in ’n groep, maar begin eers alleen. Trek drie reghoekige driehoeke van verskillende vorms en groottes. Werk so akkuraat moontlik. As jy op blokkiespapier werk, is dit baie makliker. Werk nou nog meer akkuraat en meet die drie sye van elke driehoek. Werk tot die naaste millimeter. Vul die eerste drie rye van die tabel in. Gebruik nou ’n sakrekenaar om die tabel te voltooi.

SIMBOOL DRIEHOEK A DRIEHOEK B DRIEHOEK C
Lengte van die kortste sy a .................... .................... ....................
Lengte van middelste sy b .................... .................... ....................
Lengte van die langste sy c .................... .................... ....................
Kwadraat van lengte van kortste sy a 2 .................... .................... ....................
Kwadraat van lengte van middelste sy b 2 .................... .................... ....................
Som van die boonste twee kwadrate a 2 + b 2 .................... .................... ....................
Kwadraat van lengte van langste sy c 2 .................... .................... ....................

1.2 Daar behoort iets aan te gaan met die waardes in die gemerkte blokkies. In die groep, skryf neer presies wat julle waarneem en (as julle kan) wat die rede is.

  • ’n Mens kan die drie gegewe lyne gebruik om ’n reghoekige driehoek te vorm.

Uitknipwerk:

2.1 Kan ’n mens die drie gegewe vierhoeke ook gebruik om ’n driehoek te vorm?

3. Som die uitslag van hierdie ondersoek netjies op.

einde van ONDERSOEK

Die Stelling van Pythagoras lui:

  • In ’n reghoekige driehoek is die kwadraat van die skuinssy se lengte gelyk aan die som van die kwadrate van die lengtes van die ander twee sye.

Die belangrikheid van die Stelling van Pythagoras is dat ons dit op twee maniere gebruik: Eerstens, as ons weet dat ’n driehoek reghoekig is, dan kan ons iets belangriks sê oor die lengtes van die sye. Tweedens, as ons weet dat die drie sye van ’n driehoek die gegewe verband met mekaar het, dan moet die driehoek reghoekig wees.

KLASWERK

1. Ons benoem driehoeke soos volg:

  • Verwys na die skets hierlangs.
  • Die drie hoekpunte kry hoofletters as name. ( A , B en C )
  • Die sye kan benoem word as die twee hoekpuntewaartussen die sy lê ( AB , BC en AC ), of kleinletterskan gebruik word, dikwels dieselfde kleinletter as diehoekpunt oorkant die sy ( a , b en c ).
  • Ons werk hier met reghoekige driehoeke, maar hierdiebenoeming werk vir ander driehoeke ook.
  • Ons gebruik dieselfde letters vir beide die naam van ’n sy en vir die lengte van die sy.
  • Bv. PR = 3,5 cm of r = 5 cm.Δ PRS beteken: driehoek PRS

ONTHOU om altyd ’n liniaal te gebruik vir mooi sketse!

  • In die volgende oefeninge is die eerste probleem telkens ’n voorbeeld.

2. Probleem : Driehoek AEH het ’n regte hoek by H . AH = 6 cm en EH = 8 cm.Maak ’n skets (nie akkuraat nie) van die driehoek engebruik die Stelling van Pythagoras om die lengte vansy AE te bereken.

Oplossing : Omdat ons weet dat die driehoek ’nregte hoek het, mag ons sê dat AE 2 = AH 2 + EH 2 (of: h 2 = e 2 + a 2 )

Substitusie: AH 2 + EH 2 = (6) 2 + (8) 2 = 36 + 64 = 100 cm 2 As, dus, AE 2 = 100 cm 2 , dan is AE 10 cm.

Questions & Answers

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.
Bharti
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Damian Reply
absolutely yes
Daniel
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Maciej
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Anassong
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
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
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Sanket Reply
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Damian Reply
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Cied
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abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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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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