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Hey Shankar — ready when you are. Haya, hizi hapa suluhisho za maswali yako: 1) Mathematics Assignment Kutokana na urefu wa pande za pembetatu ABC (AB = 9 cm, BC = 12 cm, AC = 15 cm), tunaweza kuthibitisha kuwa ni pembetatu mraba kwa kutumia kanuni ya Pythagoras: 9^2 + 12^2 = 81 + 144 = 225 15^2 = 225 Kwa kuwa 9^2 + 12^2 = 15^2, pembetatu ABC ni pembetatu mraba, na angle B ni 90^. Upande AC ndio hypotenuse na pia kipenyo cha duara. a) Calculate the area of the triangle ABC Step 1: Tumia fomula ya eneo la pembetatu mraba. Eneo la pembetatu = (1)/(2) × base × height Area = (1)/(2) × AB × BC Step 2: Badilisha thamani za AB na BC. Area = (1)/(2) × 9\, cm × 12\, cm Step 3: Hesabu eneo. Area = (1)/(2) × 108\, cm^2 Area = 54\, cm^2 The area of the triangle ABC is 54 cm^2. b) The size of angle BAC Step 1: Tumia uwiano wa trigonometric katika pembetatu mraba. Tunajua AB = 9\, cm, BC = 12\, cm, na AC = 15\, cm. Tunatumia ( BAC) = OppositeHypotenuse = (BC)/(AC). ( BAC) = (12)/(15) = (4)/(5) Step 2: Tafuta thamani ya angle BAC. BAC = ((4)/(5)) BAC ≈ 53.13^ The size of angle BAC is 53.13^. c) The radius of the circle Step 1: Kipenyo cha duara ni upande AC. Kipenyo D = AC = 15\, cm. Step 2: Radius ni nusu ya kipenyo. Radius r = (D)/(2) = 15\, cm2 r = 7.5\, cm The radius of the circle is 7.5\, cm. d) The area of shaded regions Step 1: Eneo la duara. Eneo la duara = r^2. Area of circle = × (7.5\, cm)^2 Area of circle = × 56.25\, cm^2 Area of circle ≈ 176.71\, cm^2 Step 2: Eneo la sehemu iliyotiwa kivuli ni eneo la duara kutoa eneo la pembetatu. Area of shaded region = Area of circle - Area of triangle ABC Area of shaded region = 176.71\, cm^2 - 54\, cm^2 Area of shaded region = 122.71\, cm^2 The area of the shaded regions is 122.71\, cm^2. 2) Two lines L1 and L2 intersect at a point M L1: 2y - 3x - 6 = 0 L2: 3y + x - 20 = 0 i) Find the coordinates of M Step 1: Andika upya milinganyo. (1) 2y - 3x = 6 (2) 3y + x = 20 Step 2: Tumia njia ya kuondoa (elimination method). Zidisha mlinganyo (2) kwa 3 ili kuondoa x. 3 × (3y + x) = 3 × 20 (3) 9y + 3x = 60 Step 3: Ongeza mlinganyo (1) na mlinganyo (3). (2y - 3x) + (9y + 3x) = 6 + 60 11y = 66 Step 4: Tafuta thamani ya y. y = (66)/(11) y = 6 Step 5: Badilisha thamani ya y = 6 katika mlinganyo (2) ili kupata x. 3(6) + x = 20 18 + x = 20 x = 20 - 18 x = 2 The coordinates of M are (2, 6). Send me the next one 📸