This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya master, twende na maswali haya. 16. Molly paid an interest of sh. 150,000 after borrowing sh. 450,000 at 20% per annum. Calculate the time she took to pay the money. Hatua ya 1: Andika fomula ya riba rahisi na utambue vigezo. Fomula ya riba rahisi ni I = PRT, ambapo: I = Riba (Interest) = sh. 150,000 P = Kiasi kikuu (Principal) = sh. 450,000 R = Kiwango cha riba (Rate) = 20% kwa mwaka = 0.20 T = Muda (Time) = ? Hatua ya 2: Badilisha vigezo kwenye fomula na utatue kwa T. 150,000 = 450,000 × 0.20 × T 150,000 = 90,000 × T Gawanya pande zote mbili kwa 90,000: T = (150,000)/(90,000) T = (15)/(9) Rahisisha sehemu: T = (5)/(3) miaka T = 1(2)/(3) miaka Muda aliochukua kulipa pesa ni: 123 miaka 17. Peter is twice as old as James. The difference of their ages is 18 years. Find James' age. Hatua ya 1: Unda milinganyo kulingana na taarifa. Acha umri wa Peter uwe P na umri wa James uwe J. "Peter ana umri mara mbili ya James": P = 2J (Mlinganyo 1) "Tofauti ya umri wao ni miaka 18": P - J = 18 (Mlinganyo 2) Hatua ya 2: Badilisha Mlinganyo 1 kwenye Mlinganyo 2 na utatue kwa J. Badilisha P na 2J katika Mlinganyo 2: 2J - J = 18 J = 18 Umri wa James ni: Miaka 18 18. A motorist drove at 120km/ hour from town P to town Q for 80 minutes. Calculate the distance he covered. Hatua ya 1: Badilisha muda kutoka dakika kwenda masaa. Kasi imetolewa kwa km/saa, kwa hivyo muda lazima uwe katika masaa. 80 dakika = (80)/(60) masaa = (4)/(3) masaa Hatua ya 2: Tumia fomula ya umbali. Umbali = Kasi × Muda Umbali = 120 km/saa × (4)/(3) masaa Umbali = (120 ÷ 3) × 4 km Umbali = 40 × 4 km Umbali = 160 km Umbali aliosafiri ni: 160 km 19. A circular tank has a circumference of 1320cm. Find its diameter. (take as (22)/(7)) Hatua ya 1: Andika fomula ya mduara na utambue vigezo. Fomula ya mduara (circumference) ni C = d, ambapo: C = Mduara = 1320 cm = (22)/(7) d = Kipenyo (diameter) = ? Hatua ya 2: Badilisha vigezo kwenye fomula na utatue kwa d. 1320 = (22)/(7) × d Ili kutafuta d, zidisha pande zote mbili kwa (7)/(22): d = 1320 × (7)/(22) d = (1320)/(22) × 7 d = 60 × 7 d = 420 cm Kipenyo cha tanki ni: 420 cm 20. The prime factors of 72 is 2^3 × p^2. Work out the value of p. Hatua ya 1: Tafuta vigawo vikuu vya 72. Anza kugawanya 72 kwa nambari kuu ndogo zaidi: 72 ÷ 2 = 36 36 ÷ 2 = 18 18 ÷ 2 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1 Kwa hiyo, vigawo vikuu vya 72 ni 2 × 2 × 2 × 3 × 3. Hatua ya 2: Andika vigawo vikuu katika mfumo wa vipeo na ulinganishe. 72 = 2^3 × 3^2 Tunapewa kuwa 72 = 2^3 × p^2. Kwa kulinganisha milinganyo miwili, tunaona kwamba p^2 = 3^2. Hii inamaanisha p = 3. Thamani ya p ni: 3 Last free one today — make it count tomorrow, or type /upgrade for unlimited.