10 mau laʻana o nā nīnau kikowaena o ke kaumaha
1. Nā Hoʻonohonoho Kikowaena o ke koʻikoʻi ʻO ka mea e pili ana i ka kiko 0 he…
Pahana
Ua ʻike ʻia :
ʻĀpana o ka mea (A) = (8)(4) = 32
ʻO ke kiko waena ma ke axis-x (x) = ½ (8) = 4
ʻO ke kiko waena ma ke axis y (y) = ½ (4) = 2
Ua nīnau ʻia : Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka kiko 0
Pane :
2. Kahi kikowaena o ke kaumaha o kahi mea i ka helu 0 ʻo ia…
Pahana
ʻO ka mea mua, e helu i ke kiʻekiʻe o ka mea. E puʻunaue i ka mea i ʻelua mau huinakolu ʻākau, kahi o kēlā me kēia huinakolu ʻākau he 4 cm ke kumu a he 5 cm ka hypotenuse.
Ua ʻike ʻia :
ʻĀpana o ka mea (A) = ½ (kumu)(kiʻekiʻe) = ½ (8)(3) = (4)(3) = 12
ʻO ke kiko waena ma ke axis-x (x) = ½ (8) = 4
ʻO ke kiko waena ma ke axis-y (y)= 1/3 (3) = 1
Ua nīnau ʻia : Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka kiko 0
Pane :
ʻO nā hoʻonohonoho o ke kikowaena o ka umekaumaha o ka mea he (4, 1) cm.
3. E nānā i ke kiʻi ma lalo! E hoʻoholo (a) i kahi o ke kikowaena o ka umekaumaha o ka mea e pili ana i ke kiko P (b) i kahi o ke kikowaena o ka umekaumaha o ka mea e pili ana i ka ʻaoʻao PQ.
Pahana
Ua ʻike ʻia :
E puʻunaue i ka mea i ʻelua ʻāpana, ʻāpana 1 = huinahā like, ʻāpana 2 = huinahā like.
A1 = (6)(2) = 12
A2 = (2)(2) = 4
x1 = ½ (6) = 3
x2 = ½ (2) + 2 = 1 + 2 = 3
y1 = ½ (2) = 1
y2 = ½ (2) + 2 = 1 + 2 = 3
Ua nīnau ʻia : Nā hoʻonohonoho o ke kikowaena o ke kaumaha e pili ana i ka ʻaoʻao PQ
Pane :
(a) ʻO ke kikowaena o ka umekaumaha o ka mea e pili ana i ke kiko P ʻo (3; 1,5) cm.
(b) ʻO ke kūlana o ke kikowaena o ke kaumaha o ka mea e pili ana i ka ʻaoʻao PQ he 1,5 cm
4. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2015/2016 Helu 10
E nānā i ke kiʻi ma lalo nei!
ʻO nā kikowaena o ke kikowaena o ka umekaumaha o ka mokulele ʻano H...
A. (3; 4)
B. (3,5 ; 2,5)
C. (3,5 ; 4)
D. (4; 3)
E. (4; 4)
Pahana
E hoʻokaʻawale i ka mea i ʻekolu ʻāpana.
ʻĀpana o ka ʻāpana 1 (A 1 ) = (2)(6) = 12 kenimika 2
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-x (x 1 ) = 1/2 (2) = 1 kenimika
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-y (y 1 ) = 1/2 (6) = 3 kenimika
ʻĀpana o ka ʻāpana 2 (A 2 ) = (4)(2) = 8 kenimika 2
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-x (x 2 ) = 2 + (1/2)(4) = 2 + 2 = 4 kenimika
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-y (y 2 ) = 2 + (1/2)(2) = 2 + 1 = 3 kenimika
ʻĀpana o ka ʻāpana 3 (A 3 ) = (2)(6) = 12
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-x (x 3 ) = 2 + 4 + (1/2)(2) = 2 + 4 + 1 = 7 kenimika
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-y (y 3 ) = 1/2 (6) = 3 kenimika
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-x:
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-y:
ʻO nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mokulele ʻano H ʻo (x, y) = (4, 3)
ʻO D ka pane pololei.
5. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2014/2015 Helu 6
E nānā i ka ʻāpana like me nā ana e like me ka mea i hōʻike ʻia ma ke kiʻi!
ʻO ke kūlana o ke kikowaena o ke kaumaha o ke kinona ma luna e pili ana i ka axis-x ʻo ia….
A. 2,0 kenimika
B. 2,5 kenimika
C. 3,0 kenimika
D. 3,5 kenimika
E. 4,0 kenimika
Pahana
E puʻunaue i ka mea i 4 ʻāpana, ʻo ia hoʻi ʻo A, B, C a me D.
E helu i ka ʻāpana o kēlā me kēia ʻāpana.
A A = ½ (kumu)(kiʻekiʻe) = ½ (1,5)(3) = (1,5)(1,5) = 2,25
A B = (lōʻihi)(ākea) = (4,5-1,5)(1) = (3)(1) = 3
AC = ½ (kumu)(kiʻekiʻe) = ½ (6-4,5)(3) = (1,5)(1,5) = 2,25
A D = ½ (kumu)(kiʻekiʻe) = ½ (4,5-1,5)(6-3) = ½ (3)(3) = (1,5)(3) = 4,5
y A = 1/3 (3) = 1
yB = 1/2 (1) = 0,5
yC = 1/3 (3) = 1
yD = 3 + (1/3)(6-3) = 3 + (1/3)(3) = 3 + 1 = 4
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-y:
ʻO ke kūlana o ke kikowaena o ke kaumaha o ke kinona e pili ana i ka axis-x he 2 kenimika.
ʻO A ka pane pololei.
6. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2014/2015 Helu 6
E nānā i ke kiʻi!
ʻO nā hoʻonohonoho o ke kikowaena o ke koʻikoʻi o ke kiʻi ma lalo nei….
Pahana
E puʻunaue i ka mea i 4 ʻāpana, ʻo ia hoʻi ʻo A, B, C a me D.
E helu i ka ʻāpana o kēlā me kēia ʻāpana.
AA = (lōʻihi)(ākea) = (4)(3) = 12
A B = ½ (kumu)(kiʻekiʻe) = ½ (6-4)(3) = ½ (2)(3) = (1)(3) = 3
A C = ½ (kumu)(kiʻekiʻe) = ½ (8-6)(3) = ½ (2)(3) = (1)(3) = 3
A D = (lōʻihi)(ākea) = (8)(6-3) = (8)(3) = 24
y A = 1/2 (3) = 1,5
y B = 3 – (1/3)(3) = 3 – 1 = 2
y C = 3 – (1/3)(3) = 3 – 1 = 2
yD = 3 + (1/2)(6-3) = 3 + (1/2)(3) = 3 + 1,5 = 4,5
x A = 1/2 (4) = 2
x B = 4 + (1/2)(6-4) = 4 + (1/2)(2) = 4 + 1 = 5
x C = 6 + (1/2)(8-6) = 6 + (1/2)(2) = 6 + 1 = 7
x D = 1/2 (8) = 4
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-x:
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-y:
ʻO ka pane pololei ʻo B.
7. ʻO nā hoʻonohonoho o ke kikowaena o ka umekaumaha o ka mea like ma ke kiʻi ma lalo nei...
A. (14, 15)
B. (17, 11)
C. (15, 11)
D. (15, 7)
E. (11, 7)
Kūkākūkā:
E hoʻokaʻawale i ka mea i ʻekolu ʻāpana, nona nā wahi (10-0)x(10-0), (20-10)x(30-0), (30-20)x(10-0) kēlā me kēia.
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka axis-x:
x1 = ka mamao o ke kikowaena o ka ʻāpana 1 mai ke kiko 0, x2 = ka mamao o ke kikowaena o ka ʻāpana 2 mai ke kiko 0, x3 = ka mamao o ke kikowaena o ka ʻāpana 3 mai ke kiko 0.
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka axis-y:
y1 = ka mamao o ke kikowaena o ka ʻāpana 1 mai ke kiko 0, y2 = ka mamao o ke kikowaena o ka ʻāpana 2 mai ke kiko 0, y3 = ka mamao o ke kikowaena o ka ʻāpana 3 mai ke kiko 0.
ʻO nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea (15, 11)
ʻO C ka pane pololei.
8. ʻO nā hoʻonohonoho o ke kikowaena o ka umekaumaha o ka mea ma ke kiʻi ma lalo nei...
A. (3; 2,7) m
B. (3 ; 3,6) m
C. (3 ; 4,0) m
D. (3 ; 4,5) mika
E. (3 ; 5,0) m
Kūkākūkā:
E hoʻokaʻawale i ka mea i ʻelua ʻāpana, nona ka nui o (5-1)x(3-0), ½ (6-0)x(9-3)
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka axis-x:
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ka axis-y:
ʻO nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea (3; 3,6)
ʻO ka pane pololei ʻo B.
9. ʻO nā hoʻonohonoho o ke kikowaena o ke kaumaha o kahi mea like e pili ana i ke kiko O ma ke kiʻi aʻe nei ...
A. (4 3/5, 3 3/5)
B. (4 1/3, 3 1/3)
C. (4 1/3, 3)
D. (3 1/3, 4 1/3)
E. (3, 3 2/3)
Pahana
E puʻunaue i ka mea i ʻekolu ʻāpana, ʻāpana 1 = huinahā like, ʻāpana 2 = huinahā like, ʻāpana 3 = huinahā like.
ʻĀpana o ka ʻāpana 1 (A1) = (2-0)(8-0) = (2)(8) = 16
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-x (x1) = 1
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-y (y1) = 4
ʻĀpana o ka ʻāpana 2 (A2) = (4-2)(2-0) = (2)(2) = 4
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-x (x2) = 3
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-y (y2) = 1
ʻĀpana o ka ʻāpana 3 (A3) = (6-4)(8-0) = (2)(8) = 16
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-x (x3) = 5
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-y (y3) = 4
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-x:
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-y:
ʻO nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea e pili ana i ke kiko O ʻo (x, y) = (3, 3 2/3)
ʻO ka pane pololei ʻo E.
10. ʻO nā hoʻonohonoho o ke kikowaena o ke koʻikoʻi o ke kiʻi mokulele ma lalo nei….
A. (1 1/2, 1 1/2) kenimika
B. (2.1/2) kenimika
C. (2, 1 1/2) kenimika
D. (2 1/2, 1 1/2) kenimika
E. (2 1/2, 2 1/2) kenimika
Pahana
E puʻunaue i ka mea i ʻekolu ʻāpana, ʻāpana 1 = huinahā like, ʻāpana 2 = huinahā like, ʻāpana 3 = huinahā like.
ʻĀpana o ka ʻāpana 1 (A1) = (1-0)(3-0) = (1)(3) = 3
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-x (x1) = 0,5
ʻO ke kiko waena o ka ʻāpana 1 ma ke axis-y (y1) = 1,5
ʻĀpana o ka ʻāpana 2 (A2) = (3-1)(2-1) = (2)(1) = 2
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-x (x2) = 2
ʻO ke kiko waena o ka ʻāpana 2 ma ke axis-y (y2) = 1,5
ʻĀpana o ka ʻāpana 3 (A3) = (4-3)(3-0) = (1)(3) = 3
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-x (x3) = 3,5
ʻO ke kiko waena o ka ʻāpana 3 ma ke axis-y (y3) = 1,5
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-x:
Nā hoʻonohonoho o ke kikowaena o ke kaumaha o ka mea ma ke axis-y:
ʻO nā hoʻonohonoho o ke kikowaena o ka umekaumaha o ka mea (x, y) = (2, 1 1/2)
ʻO C ka pane pololei.
Puna nīnau:
Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana
