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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Huu hapa ni ufumbuzi wa maswali yako: 10. Step 1: Tafuta vigawo vikuu vya kila namba. Ili kujua ni lini mashine zitatuma ishara kwa wakati mmoja tena, tunahitaji kutafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha vipindi vyao. 24 = 2^3 × 3 27 = 3^3 30 = 2 × 3 × 5 50 = 2 × 5^2 Step 2: Hesabu LCM. LCM ni zao la vigawo vikuu vyote vilivyoinuliwa kwa nguvu zao za juu zaidi. LCM(24, 27, 30, 50) = 2^3 × 3^3 × 5^2 LCM = 8 × 27 × 25 LCM = 216 × 25 = 5400 sekunde Step 3: Badilisha sekunde kuwa masaa na dakika. 5400 sekunde = (5400)/(60) dakika = 90 dakika 90 dakika = 1 saa na 30 dakika Step 4: Ongeza muda huu kwenye muda wa kuanzia. Mashine zilituma ishara kwa wakati mmoja saa 5:00 jioni. Muda unaofuata = 5:00 jioni + 1 saa 30 dakika = 6:30 jioni Mashine zitatuma ishara kwa wakati mmoja tena saa 6:30 jioni. 11. Step 1: Weka usemi katika fomu ya logariti. Acha x = 4/(75.63). x = ( (37^2 × 0.0168)/(75.63) )^(1)/(4) x = (1)/(4) [2 37 + 0.0168 - 75.63] Step 2: Tafuta logariti za namba. Kutoka kwenye jedwali la logariti: 37 = 1.5682 0.0168 = 2.2253 75.63 = 1.8787 Step 3: Hesabu sehemu ya nambari. 2 37 = 2 × 1.5682 = 3.1364 (nambari ya juu) = 3.1364 + 2.2253 = 1.3617 Step 4: Hesabu logariti ya usemi mzima. ((37^2 × 0.0168)/(75.63)) = 1.3617 - 1.8787 1.3617 - 1.8787 = -0.5170 Ili kuandika kwa tabia yenye bar: -0.5170 = -1 + 0.4830 = 1.4830 Step 5: Gawanya kwa 4. x = (1)/(4) (1.4830) Ili kugawanya, tunabadilisha tabia ili iweze kugawanyika kwa 4: 1.4830 = -4 + 3.4830 x = (-4 + 3.4830)/(4) = -1 + 0.87075 x = 1.8708 (kwa sehemu nne za desimali) Step 6: Tafuta antilogariti. Kutoka kwenye jedwali la antilogariti, mantissa 0.8708 inatoa 7427. Tabia 1 inamaanisha kuna sifuri moja kabla ya desimali. x = 0.7427 Thamani ya usemi ni 0.7427. 12. Step 1: Hesabu ujazo wa chuma. Tunajua msongamano () = Masi (m) / Ujazo (V). Hivyo, V = (m)/(). V = 63 Kg7000 Kg/m^3 = 0.009 m^3 Step 2: Hesabu eneo la nje la msalaba wa bomba. Vipimo vya nje: 12 cm na 15 cm. Badilisha kuwa mita: 12 cm = 0.12 m 15 cm = 0.15 m Eneo la nje = 0.12 m × 0.15 m = 0.018 m^2 Step 3: Hesabu eneo la ndani la msalaba wa bomba. Vipimo vya ndani: 10 cm na 12 cm. Badilisha kuwa mita: 10 cm = 0.10 m 12 cm = 0.12 m Eneo la ndani = 0.10 m × 0.12 m = 0.012 m^2 Step 4: Hesabu eneo la msalaba wa chuma (ukuta wa bomba). Eneo la chuma = Eneo la nje - Eneo la ndani Eneo la chuma = 0.018 m^2 - 0.012 m^2 = 0.006 m^2 Step 5: Hesabu urefu wa bomba. Ujazo wa chuma = Eneo la chuma × Urefu wa bomba (L) L = Ujazo wa chumaEneo la chuma L = 0.009 m^30.006 m^2 = 1.5 m Urefu wa bomba ni 1.5 m. 3 done, 2 left today. You're making progress.