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
Huu hapa ni ufumbuzi wa swali la 5: Ili kutatua swali hili "kwa kuchora", tutatumia kanuni za mteremko wa mistari iliyo wima (perpendicular lines) kwenye ndege ya Cartesian. Mistari miwili ikiwa wima, bidhaa ya miteremko yao ni -1. Step 1: Tafuta mteremko wa mstari wa kwanza (L1). Mstari wa kwanza unapita kwenye pointi (-1, 1) na (3, 2). Kanuni ya mteremko m = (y_2 - y_1)/(x_2 - x_1). m_1 = (2 - 1)/(3 - (-1)) = (1)/(3 + 1) = (1)/(4) Mteremko wa mstari wa kwanza ni (1)/(4). Step 2: Tafuta mteremko wa mstari wa pili (L2). Mstari wa pili unapita kwenye pointi (2, -2) na (0, m). m_2 = (m - (-2))/(0 - 2) = (m + 2)/(-2) Mteremko wa mstari wa pili ni (m + 2)/(-2). Step 3: Tumia masharti ya mistari iliyo wima. Kwa kuwa mistari hiyo miwili ni wima, bidhaa ya miteremko yao ni -1. m_1 · m_2 = -1 (1)/(4) · (m + 2)/(-2) = -1 Step 4: Tatua kwa m. (m + 2)/(-8) = -1 Panua pande zote mbili kwa -8: m + 2 = (-1) × (-8) m + 2 = 8 Toa 2 kutoka pande zote mbili: m = 8 - 2 m = 6 Thamani ya m ni 6. Tuma swali linalofuata 📸