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Tuesday, July 30, 2013
ENEO LA PEMBETATU-5
Tafuta eneo la pembetatu ifuatayo
Suluhu
Eneo =
1
x kitako x kimo
2
Eneo =
1
x 48 x 10
2
Eneo =
1
x
48
24
x 10
2
1
Eneo = 1 x 24 x 10
Eneo = 240
Hivyo eneo ni dm
2
240
NYUZI-5
Tafuta thamani ya a katika umbo lifuatalo
Suluhu
2a + a + 90
0
= 180
0
3a + 90
0
= 180
0
3a + 90
0
- 90
0
= 180
0
- 90
0
3a + 0
0
= 90
0
3a = 90
0
3a
=
90
0
3 3
a = 30
0
Hivyo thamani ya a ni nyuzi 30
ENEO LA MCHE MSTATILI-4
Tafuta eneo la mche mstatili ufuatao:
Suluhu
Eneo= (urefu x 2) + (upana x 2) + (kimo x 2)
= (40x2) + (8x2) + (10 x 2)
=80 + 16 + 20
=116
Hivyo eneo ni m
2
116
MZINGO WA DUARA-7
Tafuta mzingo wa duara hapo chini
Suluhu
Mzingo = ∏ x D
=
22
x
140
70
7
1
= 22 x 70
= 1540
Hivyo mzingo ni milimeta 1540.
NYUZI-4
Tafuta thamani ya a katika umbo lifuatalo:
Suluhu
3a + 3a + (a + 20) + (a + 20) = 360
6a + (a + 20) + (a + 20) = 360
6a + 2a + 40 = 360
8a + 40 = 360
8a = 360 – 40
8a = 320
8a
=
320
8 8
a= 40
Hivyo thamani ya a ni 40
ALJEBRA 16
Ikiwa 6y = 20; tafuta thamani ya y
Solution
6y = 20
6y
=
20
gawanya kwa 6 kila upande
6 6
y =20/6 = 3
2
/6 = 3
1
/3
Hivyo y = 3
1
/3
PYTHAGORAS-6
Tafuta urefu AC
Suluhu
Tutatumia kanuni ya PYTHAGORAS [ a
2
+ b
2
= c
2
]
a
2
+ b
2
= c
2
AB
2
+ BC
2
= AC
2
60
2
+ 25
2
= AC
2
3600 + 625 = AC
2
4225 = AC
2
[Tafuta kipeuo cha pili cha 4225]
65 = AC
Hivyo AC= sm 65
ENEO LA MSTATILI-3
Eneo la mstatili ni sm
2
800. Tafuta upana ikiwa urefu wake ni sm 80.
Suluhu
Chukulia kwamba upana ni w
Eneo= urefu x upana
800 = w x 80
800
=
80w
80 80
w = 10
Hivyo upana ni sm 10
ENEO LA MSAMBAMBA-2
Eneo la msambamba ni sm
2
80. Tafuta kitako ikiwa kimo ni sm 10.
Suluhu
Chukulia kwamba kitako ni e
Eneo= kitako x kimo
80 = e x 10
80
=
10e
10 10
e = 8
Hivyo kitako ni sm 8
NYUZI-3
Tafuta thamani ya n katika umbo lifuatalo:
Suluhu
n + n + (n + 4) + (n + 4) = 360
4n + 8 = 360
4n = 352
4n
=
352
4 4
n = 88
Hivyo thamani ya n ni 88
KIPEUO CHA PILI-1
Tafuta kipeuo cha pili cha kwa kutumia vigawo tasa.
suluhu
Hivyo kipeuo cha pili ni 16
Monday, July 29, 2013
PYTHAGORAS-5
Tafuta urefu AC
Suluhu
Tutatumia kanuni ya PYTHAGORAS [ a
2
+ b
2
= c
2
]
a
2
+ b
2
= c
2
AB
2
+ BC
2
= AC
2
24
2
+ 10
2
= AC
2
576 + 100 = AC
2
676 = AC
2
[Tafuta kipeuo cha pili cha 676]
26 = AC
Hence AC is 26cm
MZINGO WA MRABA-9
Mzingo wa mraba ni sm 88. Tafuta urefu wa upande mmoja.
Suluhu
Hebu chukulia kwamba upande = G
Mzingo = 4 x upande
88 = 4 x G
88
=
4G
4 4
a = 22
Hivyo upande mmoja ni mm 22
ALJEBRA-15
Ikiwa
1P
= 50; tafuta m
13
Suluhu
1P
= 50
13
1
13
x
1P
= 50 x 13 zidisha kwa 13 kila upande
1
13
1P = 50 x 13
P = 650
Hivyo m=650
MZINGO WA NUSU DUARA-2
Tafuta mzingo wa nusu duara ifuatayo
Suluhu
Mzingo =
∏
D
+ D
2
Mzingo =
11
22
X
50
350
+ 350
1
7
1
2
= (11 x 50 ) + 350
= 550 + 350
= 900
Hivyo mzingo ni m 900
PYTHAGORAS-4
Tafuta urefu AC
Suluhu
Tutatumia kanuni ya PYTHAGORAS [ a
2
+ b
2
= c
2
]
a
2
+ b
2
= c
2
AB
2
+ BC
2
= AC
2
25
2
+
36
2
= AC
2
625
+
3600
= AC
2
4225 = AC
2
[Tafuta kipeuo cha pili cha 4225]
65 = AC
Hivyo AC= sm 65
ENEO LA MSAMBAMBA-2
Tafuta eneo la msambamba ufuatao
Suluhu
Eneo = kitako x kimo
= 12 x 5
=60
Hivyo Eneo ni mm
2
60
MZINGO WA DUARA-6
Tafuta mzingo wa duara hapo chini
Solution
Mzingo = 2 x ∏ x r
= 2 x
22
x
630
90
7
1
= 2 x 22 x 90
= 44 x 90
= 3960
Hivyo mzingo ni meta 3960.
ENEO LA DUARA-5
Tafuta eneo la duara lifuatalo
Suluhu
Eneo = ∏ x r
2
=
22
x
56
8
x 56
7
1
=22 x 8 x 56
=176 x 56
=9856
Hivyo eneo ni m
2
9856
MZINGO WA MRABA-8
Tafuta mzingo wa mraba hapo chini
Suluhu
Mzingo = 4 x upande
= 4 x 200
= 800
Hivyo mzingo ni mm 800
PYTHAGORAS-3
Tafuta urefu AC
Suluhu
Tutatumia kanuni ya PYTHAGORAS [ a
2
+ b
2
= c
2
]
a
2
+ b
2
= c
2
AB
2
+ BC
2
= AC
2
5
2
+ 12
2
= AC
2
25 + 144 = AC
2
169 = AC
2
[Tafuta kipeuo cha pili cha 169]
13 = AC
Hivyo AC= sm 13
NYUZI-2
Tafuta thamani ya x katika umbo lifuatalo.
Solution
2x + 2x + 8x + 8x = 360
0
4x + 16x = 360
0
20x = 360
0
20x
=
360
0
20 20
X = 18
0
Hivyo x ni 18
0
Friday, July 26, 2013
ENEO LA MCHE DUARA-2
Tafuta eneo la mche duara ufuatao (umefungwa pande zote)
Suluhu
Eneo = 2∏rh + 2∏ x r
2
=(2 x
22
x
35
5
x 100) + (2 x
22
x
35
5
x 35)
7
1
7
1
=(2 x 22 x 5 x 100) + (2 x 22 x 5 x 35)
=(44 x 500) + (44 x 5 x 35)
=22000+ 7700
=29700
Hivyo eneo ni sm
2
29700
Wednesday, July 24, 2013
ENEO LA PEMBETATU-4
Tafuta eneo la pembetatu ifuatayo
Suluhu
Eneo =
1
x kitako x
kimo
2
Eneo =
1
x
22
x
20
2
Eneo =
1
x
22
11
x
20
2
1
Eneo =
1 x 11
x
20
Eneo =
220
Hivyo eneo ni mm
2
220
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