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.
ScanSolve AI Answer
Hapa kuna suluhisho la maswali uliyotuma: 1. Rahisisha kabisa (2x^2 + x - 3)/(4x^2 - 9) Hatua ya 1: Rahisisha nambari (numerator). Nambari ni 2x^2 + x - 3. Tunaweza kuifactor kwa kutafuta namba mbili zinazozidisha 2 × -3 = -6 na kujumlisha 1. Namba hizo ni 3 na -2. 2x^2 + x - 3 = 2x^2 + 3x - 2x - 3 = x(2x + 3) - 1(2x + 3) = (2x + 3)(x - 1) Hatua ya 2: Rahisisha denominator. Denominator ni 4x^2 - 9. Hii ni tofauti ya miraba, a^2 - b^2 = (a - b)(a + b). Hapa, a = 2x na b = 3. 4x^2 - 9 = (2x)^2 - 3^2 = (2x - 3)(2x + 3) Hatua ya 3: Rahisisha sehemu nzima. Sasa tunaweza kuandika upya sehemu na kufuta vigezo vinavyofanana. ((2x + 3)(x - 1))/((2x - 3)(2x + 3)) Futa (2x + 3) kutoka juu na chini: = (x - 1)/(2x - 3) Jibu: (x - 1)/(2x - 3) 2. Maji hutiririka kutoka kwenye bomba kwa kiwango cha lita 250 kwa dakika kuingia kwenye tanki lililojaa maji lenye vipimo vya 3.2m kwa 2.5m kwa 2m. Hesabu muda unaochukua kujaza tanki kabisa. Hatua ya 1: Hesabu ujazo wa tanki. Vipimo vya tanki ni urefu (L) = 3.2 m, upana (W) = 2.5 m, na kina (H) = 2 m. Ujazo (V) wa tanki ni: V = L × W × H V = 3.2 m × 2.5 m × 2 m V = 16 m^3 Hatua ya 2: Badilisha ujazo kutoka mita za ujazo kwenda lita. Tunajua kuwa 1 m^3 = 1000 lita. V = 16 m^3 × 1000 lita/m^3 V = 16000 lita Hatua ya 3: Hesabu muda unaochukua kujaza tanki. Kiwango cha mtiririko wa maji ni lita 250 kwa dakika. Muda (T) = Ujazo wa tanki / Kiwango cha mtiririko T = 16000 lita250 lita/dakika T = 64 dakika Jibu: 64 dakika Last free one today — make it count tomorrow, or type /upgrade for unlimited.