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Haya Shankar, hizi hapa suluhisho za maswali yako: 2) Two lines L1 and L2 intersect at a point M L1: 2y - 3x - 6 = 0 L2: 3y + x - 20 = 0 Kutoka jibu lililopita, M = (2, 6). ii) Another third line L3 is perpendicular to L2 at M. Find the equation of L3 in the form y = mx + c where m and c are constant. Step 1: Pata gradient ya L2. Andika L2 katika mfumo y = mx + c: 3y + x - 20 = 0 3y = -x + 20 y = -(1)/(3)x + (20)/(3) Gradient ya L2, m_2 = -(1)/(3). Step 2: Pata gradient ya L3. Kwa kuwa L3 ni perpendicular kwa L2, gradient yake m_3 itakuwa negative reciprocal ya m_2. m_3 = -(1)/(m_2) = -(1)/(-1)3 = 3 Step 3: Pata mlinganyo wa L3. L3 inapitia point M (2, 6) na ina gradient m_3 = 3. Tumia mfumo y - y_1 = m(x - x_1). y - 6 = 3(x - 2) y - 6 = 3x - 6 y = 3x Equation ya L3 ni y = 3x. iii) Another line L4 is parallel to line L1 and passes through C(1,3). Determine the x and y intercepts of L4. Step 1: Pata gradient ya L1. Andika L1 katika mfumo y = mx + c: 2y - 3x - 6 = 0 2y = 3x + 6 y = (3)/(2)x + 3 Gradient ya L1, m_1 = (3)/(2). Step 2: Pata gradient ya L4. Kwa kuwa L4 ni parallel kwa L1, gradient yake m_4 itakuwa sawa na m_1. m_4 = (3)/(2) Step 3: Pata mlinganyo wa L4. L4 inapitia point C (1, 3) na ina gradient m_4 = (3)/(2). Tumia mfumo y - y_1 = m(x - x_1). y - 3 = (3)/(2)(x - 1) Zidisha pande zote mbili kwa 2: 2(y - 3) = 3(x - 1) 2y - 6 = 3x - 3 2y - 3x - 3 = 0 Step 4: Pata x-intercept. Weka y = 0 katika mlinganyo wa L4. 2(0) - 3x - 3 = 0 -3x = 3 x = -1 X-intercept ni (-1, 0). Step 5: Pata y-intercept. Weka x = 0 katika mlinganyo wa L4. 2y - 3(0) - 3 = 0 2y = 3 y = (3)/(2) Y-intercept ni (0, (3)/(2)). 3) The table below shows the income tax rates for a certain year. | Taxable pay per month | Tax rate (%) | | :-------------------- | :----------- | | 1 - 9,680 | 10% | | 9,681 - 18,800 | 15% | | 18,801 - 27,920 | 20% | | 27,921 - 37,040 | 25% | | 37,041 and above | 30% | That year Marylinnet paid net tax of Ksh 4313 per month. Her total monthly taxable allowances amounted to Ksh 15,220 and he was entitled to a monthly relief of Ksh 1,062. Every month the following deductions were made: NHIF Ksh 320, Union dues Ksh 200, Sacco value shares Ksh 500. Calculate: a) Marylinnet's monthly basic salary in Ksh. Step 1: Kokotoa Kodi Kuu (Gross Tax). Kodi Kuu = Kodi Halisi (Net Tax) + Msamaha wa Kodi (Tax Relief) Kodi Kuu = Ksh 4313 + Ksh 1062 = Ksh 5375 Step 2: Kokotoa Mapato Yanayotozwa Kodi (Taxable Income) kwa kutumia Kodi Kuu. • Kodi katika bendi ya kwanza (10%): 10\% ya 9680 = 0.10 × 9680 = Ksh 968 Kodi iliyobaki = 5375 - 968 = Ksh 4407 • Kodi katika bendi ya pili (15%): Kiwango cha mapato katika bendi hii = 18800 - 9680 = Ksh 9120 15\% ya 9120 = 0.15 × 9120 = Ksh 1368 Kodi iliyobaki = 4407 - 1368 = Ksh 3039 • Kodi katika bendi ya tatu (20%): Kiwango cha mapato katika bendi hii = 27920 - 18800 = Ksh 9120 20\% ya 9120 = 0.20 × 9120 = Ksh 1824 Kodi iliyobaki = 3039 - 1824 = Ksh 1215 • Kodi katika bendi ya nne (25%): Kodi iliyobaki (Ksh 1215) inatozwa katika bendi hii. Kiasi cha mapato kilichotozwa kodi katika bendi hii = $121