Teacher Emily wrote the following operations on the board. Simplify the operations a)g b)

Karibu tena Flora! Nimeona picha yako. Wacha tuendelee na maswali haya. Problem 10: Ili kupata gradient (mteremko) wa mstari unaounganisha pointi mbili, tunatumia formula ya gradient. Step 1: Andika formula ya gradient na pointi ulizopewa. Pointi ni A(x_1, y_1) = (0,0) na B(x_2, y_2) = (4,3). Formula ya gradient ni: m = (y_2 - y_1)/(x_2 - x_1) Step 2: Badilisha thamani za pointi kwenye formula. m = (3 - 0)/(4 - 0) Step 3: Rahisisha ili kupata gradient. m = (3)/(4) Gradient ya mstari unaounganisha pointi A na B ni (3)/(4). Problem 11: Ili kurahisisha usemi huu, tutatumia sheria za vipeo (exponents) na kurahisisha namba. Step 1: Zidisha namba na vigezo (variables) kwenye nambari (numerator). (9x^7y^3 × 4x^6y^4)/(3x^2y^2) = ((9 × 4) × (x^7 × x^6) × (y^3 × y^4))/(3x^2y^2) Tumia sheria a^m × a^n = a^m+n: = 36x^7+6y^3+43x^2y^2 = 36x^13y^73x^2y^2 Step 2: Gawanya namba na vigezo kwenye denominator (kigawanyo). Tumia sheria (a^m)/(a^n) = a^m-n: = ((36)/(3)) × (x^13x^2) × ((y^7)/(y^2)) = 12x^13-2y^7-2 Step 3: Rahisisha vipeo. = 12x^11y^5 Usemi uliorahisishwa ni 12x^11y^5. Problem 12: Ili kukokotoa eneo lililoangaziwa na spotlight, tunahitaji kutumia formula ya eneo la sekta ya duara. Step 1: Tambua radius na angle. Kipenyo (diameter) D = 10 m, hivyo radius r = (D)/(2) = (10)/(2) = 5 m. Angle ya sekta = 30^. Step 2: Andika formula ya eneo la sekta. Eneo la sekta = ()/(360^) × r^2 Step 3: Badilisha thamani kwenye formula na kokotoa. Eneo = (30^)/(360^) × (5 m)^2 Eneo = (1)/(12) × (25 m^2) Eneo = (25)/(12) m^2 Step 4: Kokotoa thamani ya namba (kwa kutumia ≈ 3.14159). Eneo ≈ (25 × 3.14159)/(12) m^2 Eneo ≈ (78.53975)/(12) m^2 Eneo ≈ 6.544979 m^2 Eneo lililoangaziwa na spotlight ni takriban 6.54 m^2 (kwa desimali mbili). That's 2 down. 3 left today — send the next one.