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
Haya, nitakusaidia kutatua maswali haya. 8. Pata neno la nane na jumla ya maneno 15 ya kwanza ya AP: -7, -4, -1, Hatua ya 1: Tambua neno la kwanza (a) na tofauti ya kawaida (d). Neno la kwanza a = -7. Tofauti ya kawaida d = -4 - (-7) = -4 + 7 = 3. Hatua ya 2: Pata neno la nane (T_8) kwa kutumia fomula T_n = a + (n-1)d. T_8 = -7 + (8-1)3 T_8 = -7 + (7)3 T_8 = -7 + 21 T_8 = 14 Hatua ya 3: Pata jumla ya maneno 15 ya kwanza (S_15) kwa kutumia fomula S_n = (n)/(2)[2a + (n-1)d]. S_15 = (15)/(2)[2(-7) + (15-1)3] S_15 = (15)/(2)[-14 + (14)3] S_15 = (15)/(2)[-14 + 42] S_15 = (15)/(2)[28] S_15 = 15 × 14 S_15 = 210 Neno la nane ni 14 na jumla ya maneno 15 ya kwanza ni 210. 9. Tao la duara, lenye rediasi 10cm, linatengeneza pembe ya 80^ katikati ya duara. Pata urefu wa tao. Hatua ya 1: Tambua rediasi (r) na pembe (). Rediasi r = 10 cm. Pembe = 80^. Hatua ya 2: Tumia fomula ya urefu wa tao L = ()/(360^) × 2 r. L = (80^)/(360^) × 2 × (22)/(7) × 10 L = (8)/(36) × 2 × (22)/(7) × 10 L = (2)/(9) × (440)/(7) L = (880)/(63) L ≈ 13.968 Urefu wa tao ni takriban 13.97 cm. 10. Katika trapezi yenye eneo la 40 cm^2, uwiano wa urefu wa pande sambamba ni 2:3. Pata urefu wa pande sambamba ikiwa zimetenganishwa kwa 5cm. Hatua ya 1: Tambua eneo (A), uwiano wa pande sambamba, na urefu (h). Eneo A = 40 cm^2. Uwiano wa pande sambamba a:b = 2:3. Urefu h = 5 cm. Hatua ya 2: Wacha pande sambamba ziwe 2x na 3x. Tumia fomula ya eneo la trapezi A = (1)/(2)(a+b)h. 40 = (1)/(2)(2x + 3x)5 40 = (1)/(2)(5x)5 40 = (25x)/(2) Hatua ya 3: Tatua kwa x. 40 × 2 = 25x 80 = 25x x = (80)/(25) x = (16)/(5) x = 3.2 Hatua ya 4: Pata urefu wa pande sambamba. Upande wa kwanza a = 2x = 2 × 3.2 = 6.4 cm. Upande wa pili b = 3x = 3 × 3.2 = 9.6 cm. Urefu wa pande sambamba ni 6.4 cm na 9.6 cm. Tuma swali linalofuata 📸