Ngā Pūnaha o ngā Tauritekore Rārangi: Whakataki me ngā Whakamahinga
He ariā taketake ngā taurite kore rārangi i roto i te pāngarau, ā, he whānuitia ngā tono i roto i ngā momo mara, tae atu ki te ōhanga, te hangarau, te whakahaere, me te pūtaiao rorohiko. I roto i tēnei tuhinga, ka tūhuratia e tātou he aha ngā taurite kore rārangi, me pēhea te whakaoti i aua taurite, me ō rātou tono i te ao tūturu.
Te Mārama ki ngā Tauritekore Raina
Ko te kore taurite rārangi he kōrero e whakaatu ana he nui ake, he iti iho rānei tētahi kīanga rārangi i tētahi atu kīanga rārangi. Ka taea te whakaatu i tēnei kore taurite mā te whakamahi i tētahi, i ētahi rānei taurangi. Ko te āhua whānui o tētahi kore taurite rārangi me tētahi taurangi koia tēnei:
\[ toki + b < c \] \[ toki + b > c \]
\[ toki + b \leq c \]
\[ toki + b \geq c \]
I konei, he pūmau a \(a\), \(b\), me \(c\), ā, he taurangi a \(x\). Ka kiia tēnei taurite kore he rārangi nā te mea ka hanga e tōna kauwhata he rārangi tika i roto i te pūnaha taunga Cartesian.
Mō te take e rua ngā taurangi, ko te āhua whānui o te kore taurite rārangi e whai ake nei:
\[ toki + mā \leq c \]
\[ toki + mā \geq c \]
\[ toki + mā < c \] \[ toki + mā > c \]
I konei, he pūmau anō a \(a\), \(b\), me \(c\), engari ināianei he taurangi a \(x\) me \(y\).
Te Whakatau i ngā Tauritekore Raina
Ngā Hipanga hei Whakaoti i ngā Tauritekore Rārangi me te Taurangi Kotahi
Hei whakaoti i tētahi taurite kore rārangi i roto i tētahi taurangi, ko ngā mahi ka taea te whai ko:
1. Wehewehea ngā Taurangi: Nukuhia ngā kupu katoa kei roto ngā taurangi ki tētahi taha o te kore taurite me ngā pūmau ki tētahi taha. Ko te tikanga o tēnei ko te tāpiri, te tango, te whakarea, te wehewehe rānei mā te tau kotahi i ngā taha e rua o te kore taurite.
2. Te Wehewehe, te Whakarea rānei mā ngā Tau Pai, Tau Kino rānei: Ina wehea, ina whakareatia rānei ngā taha e rua o te tau kore taurite ki tētahi tau pai, ka noho tonu te tohu taurite. Heoi, ki te wehea, ina whakareatia rānei ngā taha e rua ki tētahi tau kino, me huri te tohu taurite.
3. Te Whakairoiro (Whiringa): Hei whakaatu i te otinga o tētahi taurite kore rārangi, ka taea e koe te tuhi i tētahi rārangi tika mai i te whārite rārangi ōrite, ka whakamārama i te horahanga e tohu ana i te otinga mā te tatau i ngā āputa i kitea.
Hei tauira, me whakaoti te kore taurite māmā e whai ake nei:
\[ 3x – 5 \geq 7 \]
Ngā taahiraa otinga:
1. Tāpirihia te 5 ki ngā taha e rua:
\[ 3x – 5 + 5 \geq 7 + 5 \]
\[ 3x \geq 12 \]
2. Wehea ngā taha e rua ki te 3:
\[ x \geq 4 \]
Nō reira, ko te otinga mō te kore taurite \( 3x – 5 \geq 7 \) ko \( x \geq 4 \).
Ngā Hipanga hei Whakaoti i ngā Tauritekore Rārangi me ngā Taurangi e Rua
Hei whakaoti i ngā taurite kore rārangi i roto i ngā taurangi e rua, ko ngā mahi e whai ake nei ko:
1. Waihangahia he Whārite Raina Ōrite: Whakakapia te tohu taurite kore ki te tohu ōrite (=). Mā tēnei ka puta te whārite o te rārangi tika.
2. Tuhia he Rārangi i roto i ngā Taunga Cartesian: Tuhia te rārangi i roto i te pūnaha taunga Cartesian.
3. Whakatauhia te Rohe Otinga: Whakatauhia mēnā kei runga ake, kei raro iho rānei i te rārangi te otinga mō te kore taurite, i runga i te tohu kore taurite. Hei tauira, mēnā ko te kore taurite ko \( ax + by \leq c \), kei raro iho, kei te taha maui rānei o te rārangi te otinga.
4. Whakamātautau Pūwāhi: Tīpakohia he pūwāhi whakamātautau (ko te pūtake (0, 0) te tikanga mēnā kāore i runga i te rārangi) kia kite ai mēnā e tutuki ana te kore taurite. Mēnā e tutuki ana, ko te rohe kei roto taua pūwāhi te rohe otinga.
Te Whakamahinga o ngā Pūnaha Tauritekore Raina
He maha ngā whakamahinga o ngā taurite kore rārangi i roto i te oranga o ia rā, me ngā momo marautanga pūtaiao. Anei ētahi tauira:
Arotautanga Raina
I roto i te rangahau me te whakahaere mahi, ka whakamahia ngā taurite kore rārangi i roto i ngā raruraru arotau. Ko tētahi o ngā tikanga rongonui ko te Hōtaka Raina, e whakamahia ana hei whakanui, hei whakaiti rānei i tētahi mahi whāinga i raro i ngā here taurite kore rārangi. Ko ngā tono o te hōtaka raina ko:
– Whakaritenga Mahi: Me pēhea te whakarite i ngā rārangi mahi whakaputa i roto i te wheketere kia whai hua ai.
– Te Whakaiti i ngā Utu: Me pēhea te whakaiti i ngā utu i roto i ngā hongere tuku me te tohatoha.
– Te Whakanui i te Hua: Me pēhea te whakanui ake i ngā hua i roto i te pakihi me ngā rauemi me te kaha iti.
Ōhanga me te Pūtea
He maha hoki ngā whakamahinga o ngā taurite kore rārangi i roto i te ōhanga hei tauira i ngā herenga tahua me ngā rauemi. Hei tauira, i roto i te tātari tahua ā-whare, ka hiahia pea tātou ki te tauira me pēhea te tohatoha i te moni whiwhi puta noa i ngā whakapaunga rerekē (kai, reti, ratonga, me ētahi atu) i runga i te tapeke o te moni whiwhi e wātea ana.
Rangahau Pūtaiao
I roto i te pūtaiao, inā koa te ahupūngao me te matū, ka whakamahia ngā taurite kore rārangi hei whakatauira i ngā āhuatanga rerekē. Hei tauira, i roto i te thermodynamics, ka taea te whakaatu i ngā āhuatanga taurite mā te whakamahi i ngā taurite kore rārangi.
Te Hangarau me te Pūtaiao Rorohiko
I roto i te hangarau ā-iwi, ka whakamahia ngā taurite kore rārangi i roto i te hoahoa hanganga hei whakarite kia kore e neke ake ngā taumahatanga i roto i te hanganga i tētahi paepae haumaru. I roto i te pūtaiao rorohiko, ka whakamahia ngā rauropi arotau e whakamahi ana i ngā taurite kore rārangi i roto i te ako mīhini, te tātari raraunga, me ētahi atu mara.
Te Waka me te Whakahaere Rautaki
I roto i te mara o te kawe waka, ka whakamahia ngā taurite kore rārangi hei whakatauira i ngā raruraru ara waka, ko te whāinga matua he arotau i ngā ara me ngā wā haere i raro i ngā here o te kaha me te wā.
Whakamutunga
He taputapu nui ngā taurite kore rārangi i roto i te pāngarau, ā, he whānuitia hoki te whakamahinga i roto i ngā momo mara. Mā te mārama pai ki te whakaoti rapanga taurite kore rārangi me ō rātou whakamahinga mahi ka āwhina i a tātou ki te whakatau pai ake, kia whai hua ake hoki.
I tēnei ao matatini haere o ēnei rā, kei te piki haere te hiranga o te āheinga ki te whakatauira me te whakaoti rapanga o te ao tūturu mā te whakamahi i ngā taurite kore rārangi. Nō reira, me mārama pai ngā ākonga me ngā tohunga ki tēnei ariā, ā, me matatau hoki ki tōna whakamahinga.
