He tauira pātai kōrero mō te tūranga o ngā porowhita e rua

Ngā Tauira Pātai e Matapaki ana i te Tūnga o ngā Porowhita e Rua

Pendahuluan

Ko te porowhita tētahi o ngā āhua taketake o te āhuahanga e tūtaki pinepine ana tātou i roto i ngā raruraru pāngarau. He kaupapa nui te ako i te tūranga o ngā porowhita e rua nā te mea he maha ōna whakamahinga i roto i te oranga o ia rā. I roto i te pāngarau, ka taea te tātari i te tūranga o ngā porowhita e rua mā te tirotiro i ō rāua tūranga whanaunga i runga i te tawhiti i waenganui i ō rāua pokapū me ō rāua radius.

Te Ariā o te Tūnga o ngā Porowhita e Rua

Hei whakatau i te tūnga o ngā porowhita e rua, ka whakamahia e mātou ētahi tawhā matua:
1. Te pūtoro o te porowhita tuatahi (r1)
2. Te pūtoro o te porowhita tuarua (r2)
3. Te tawhiti i waenganui i ngā pokapū o ngā porowhita e rua (d)

I runga i ēnei uara, he maha ngā tūranga pea o ngā porowhita e rua:
1. He pātata te porowhita mai i waho
– Ka puta mēnā ko d = r1 + r2.
2. Ka tūtaki ngā porowhita mai i roto
– Ka puta mēnā ko d = |r1 – r2|.
3. Ngā porowhita e whakawhiti ana
– Ka puta mēnā |r1 – r2| < d < r1 + r2. 4. He motumotu ngā porowhita - Ka puta mēnā d > r1 + r2.
5. Kotahi porowhita i roto i tētahi atu porowhita, me te kore e pā
– Ka puta mēnā ko d < |r1 - r2|. 6. Ka tūtaki ngā porowhita tetahi ki tetahi - Ka puta mēnā ko d = 0, ā, ko r1 = r2 (he porowhita kotahi rāua).

Tauira Pātai me te Kōrero Me arotake tātou i ētahi tauira pātai kia pai ake ai te mārama ki te tūranga o ngā porowhita e rua. Tauira Pātai 1: Ngā Porowhita e Whakawhitiwhiti ana ki Waho Pātai: E rua ngā porowhita e rua kei ngā pūwāhi A me B ngā pokapū, ā, ko te tawhiti AB he 10 cm. Ko te radius o te porowhita tuatahi he 6 cm, ko te radius o te porowhita tuarua he 4 cm. Whakatauhia te tūranga o ngā porowhita e rua. Kōrero: - E rua: - Ko te radius o te porowhita tuatahi, r1 = 6 cm - Ko te radius o te porowhita tuarua, r2 = 4 cm - Ko te tawhiti i waenganui i ngā pokapū o ngā porowhita, d = 10 cm Mō te āhua o te pātata o waho: \[ d = r1 + r2 \] Whakauruhia ngā uara: \[ d = 6 + 4 \] \[ d = 10 \] Mai i te mea ko d = 10 cm, he ōrite ki te tapeke o r1 me r2, ka whakawhiti ngā porowhita e rua ki waho. Tauira Pātai 2: Ngā Porowhita e Whakawhitiwhiti ana ki Roto Pātai: E rua ngā porowhita he 8 cm me te 3 cm ngā radius, he 5 cm te tawhiti i waenganui i ō rāua pokapū. Whakatauhia te tūranga o ngā porowhita e rua. Kōrero: - Hoatu: - Ko te pūtoro o te porowhita tuatahi, r1 = 8 cm - Ko te pūtoro o te porowhita tuarua, r2 = 3 cm - Ko te tawhiti i waenganui i ngā pokapū o ngā porowhita, d = 5 cm Mō te āhua o te pa o roto: \[ d = |r1 - r2| \] Tātaihia: \[ d = |8 - 3| \] \[ d = 5 \] Nā te mea ko d = 5 cm, he rite ki te rerekētanga o r1 me r2, ka tūtaki ngā porowhita e rua ki roto. Tauira Pātai 3: Ngā Porowhita Whakawhiti Pātai: E rua ngā porowhita he 7 cm me te 5 cm te whānui, ā, ko te tawhiti i waenganui i ō rāua pokapū he 9 cm. Whakatauhia te tūranga o ngā porowhita e rua. Kōrero: - Hoatu: - Te whānui o te porowhita tuatahi, r1 = 7 cm - Te whānui o te porowhita tuarua, r2 = 5 cm - Te tawhiti i waenganui i ngā pokapū o ngā porowhita, d = 9 cm Mō te āhuatanga whakawhiti: \[ |r1 - r2| < d < r1 + r2 \] Tātaihia: \[ |7 - 5| < 9 < 7 + 5 \] \[ 2 < 9 < 12 \] Nā te mea kei waenganui i te |r1 - r2| me r1 + r2 te uara o d, ka tūtaki ngā porowhita e rua. Tauira Pātai 4: Ngā Porowhita Wehewehea Ngātahi Pātai: Ko ngā porowhita he 2 cm te whānui me te 3 cm te tawhiti i waenganui i ō rātou pokapū he 7 cm. Whakatauhia te tūranga o ngā porowhita e rua. Kōrero: - Hoatu: - Ko te whānui o te porowhita tuatahi, r1 = 2 cm - Ko te whānui o te porowhita tuarua, r2 = 3 cm - Ko te tawhiti i waenganui i ngā pokapū o ngā porowhita, d = 7 cm Mō ngā āhuatanga wehewehea ngātahi: \[ d > r1 + r2 \]

Tatau:
\[ 7 > 2 + 3 \]
\[ 7 > 5 \]

Nā te mea he nui ake a d i te tapeke o r1 me r2, kua wehea ngā porowhita e rua tetahi i tetahi.

Tauira Pātai 5: Porowhitahia tētahi ki roto i tētahi, kaua e pā atu

Pātai:
E rua ngā porowhita he 8 cm te whānui, ā, e 2 cm te whānui, ko te tawhiti i waenganui i ngā pokapū he 5 cm. Tāutuhia te tūranga o ngā porowhita e rua.

Kōrero:
– E mōhiotia ana:
– Ko te pūtoro o te porowhita tuatahi, r1 = 8 cm
– Ko te pūtoro o te porowhita tuarua, r2 = 2 cm
– Te tawhiti i waenganui i ngā pokapū o ngā porowhita, d = 5 cm

Mō te āhua o tētahi i roto i tētahi, me te kore e pā:
\[ d < |r1 - r2| \] Tātaihia: \[ d < |8 - 2| \] \[ 5 < 6 \] Nā te mea he iti ake a d i te rerekētanga i waenga i a r1 me r2, kei roto tetahi porowhita i tetahi atu, kāore e pā. Whakamutunga Mā te mārama ki te tūranga o ngā porowhita e rua ka āwhina i a tātou ki ngā momo whakamahinga o te āhuahanga me te mahi o te ao tūturu. Mā te mōhio ki te whanaungatanga i waenga i te radius o te porowhita me te tawhiti i waenga i ōna pokapū, ka taea e tātou te whakatau mēnā ka pā ngā porowhita e rua ki waho, ki roto rānei, ka tūtaki, ka wehe rānei. Mā ngā tauira i runga ake nei, ko te tumanako ka pai ake te mārama o ngā kaipānui ki tēnei ariā me te whakamahi i roto i ngā momo āhuatanga pāngarau. Me haere tonu te whakaharatau i ngā rapanga me ngā momo rerekētanga hei whakakoi i ō pūkenga tātari me te mārama ki te tūranga o ngā porowhita e rua. Mā te nui o tō whakaharatau, ka māmā ake ki a tātou te whakaoti rapanga maha e pā ana ki ngā porowhita i roto i te āhuahanga.