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 hapa masuluhisho ya maswali yako: a) i) Evaluate 2^5 × (1)/(2^3) Step 1: Andika (1)/(2^3) kama kielelezo hasi. (1)/(2^3) = 2^-3 Step 2: Tumia sheria ya vipeo a^m × a^n = a^m+n. 2^5 × 2^-3 = 2^5 + (-3) = 2^5-3 Step 3: Rahisisha kielelezo na hesabu. 2^5-3 = 2^2 = 4 Jibu ni 4. ii) Simplify 3x^2y^3 × 2x^3y^-1 Step 1: Panga upya maneno ili kuzidisha coefficients na vigezo tofauti. 3x^2y^3 × 2x^3y^-1 = (3 × 2) × (x^2 × x^3) × (y^3 × y^-1) Step 2: Zidisha coefficients. 3 × 2 = 6 Step 3: Tumia sheria ya vipeo a^m × a^n = a^m+n kwa vigezo x na y. x^2 × x^3 = x^2+3 = x^5 y^3 × y^-1 = y^3+(-1) = y^3-1 = y^2 Step 4: Unganisha matokeo. 6x^5y^2 Jibu ni 6x^5y^2. iii) Solve for x, given that 3x^2 - 8 = 10.75. Step 1: Ongeza 8 pande zote mbili za mlinganyo ili kutenga neno la x^2. 3x^2 - 8 + 8 = 10.75 + 8 3x^2 = 18.75 Step 2: Gawanya pande zote mbili kwa 3 ili kupata x^2. (3x^2)/(3) = (18.75)/(3) x^2 = 6.25 Step 3: Chukua mzizi wa mraba wa pande zote mbili ili kupata x. Kumbuka kuwa kuna suluhisho chanya na hasi. x = ±sqrt(6.25) x = ± 2.5 Jibu ni x = ± 2.5. 3 done, 2 left today. You're making progress.