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.
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4. Evaluate without using mathematical tables. Tunahitaji kurahisisha usemi huu kwa kubadilisha nambari za desimali kuwa sehemu au kuzidisha kwa kutumia nguvu za 10. Step 1: Badilisha nambari za desimali kuwa sehemu rahisi. sqrt((0.0625 × 2.56)/(0.25 × 0.08 × 0.5)) Tunajua kuwa: 0.0625 = (625)/(10000) = (1)/(16) 2.56 = (256)/(100) 0.25 = (25)/(100) = (1)/(4) 0.08 = (8)/(100) 0.5 = (5)/(10) = (1)/(2) Step 2: Badilisha nambari hizi kwenye usemi. sqrt((1)/(16) × (256)/(100))(1)/(4) × (8)/(100) × (1)/(2) Step 3: Rahisisha nambari ya juu (numerator) na nambari ya chini (denominator) kando. Numerator: (1)/(16) × (256)/(100) = (256)/(16 × 100) = (16)/(100) Denominator: (1)/(4) × (8)/(100) × (1)/(2) = (1 × 8 × 1)/(4 × 100 × 2) = (8)/(800) = (1)/(100) Step 4: Weka matokeo yaliyopatikana kwenye usemi wa mzizi wa mraba. sqrt((16)/(100))(1)/(100) = sqrt((16)/(100) × (100)/(1)) = sqrt(16) Step 5: Tafuta mzizi wa mraba. sqrt(16) = 4 Jibu la mwisho ni 4. 5. Solve for x in the equation (3^2x)^3 = 81 × 9^4. Tunahitaji kuandika pande zote mbili za mlinganyo kwa kutumia msingi mmoja, ambao ni 3. Step 1: Rahisisha upande wa kushoto wa mlinganyo. (3^2x)^3 = 3^2x × 3 = 3^6x Step 2: Andika nambari 81 na 9 kama nguvu za 3. 81 = 3^4 9 = 3^2 Hivyo, 9^4 = (3^2)^4 = 3^2 × 4 = 3^8. Step 3: Badilisha upande wa kulia wa mlinganyo. 81 × 9^4 = 3^4 × 3^8 Tumia sheria ya vipeo a^m × a^n = a^m+n: 3^4 × 3^8 = 3^4+8 = 3^12 Step 4: Linganisha pande zote mbili za mlinganyo. 3^6x = 3^12 Kwa kuwa besi ni sawa, tunaweza kulinganisha vipeo. 6x = 12 Step 5: Tatua kwa x. x = (12)/(6) x = 2 Jibu la mwisho ni 2. 6. After subtracting (3)/(4) from the numerator of a certain fraction and subtracting from its denominator the fraction becomes (3)/(5) (4mks) Samahani, Victor. Swali hili halijakamilika. Sehemu inayosema "and subtracting from its denominator" haijaeleza ni kiasi gani kinapaswa kutolewa kutoka kwa denominator. Tafadhali thibitisha kiasi kinachotolewa kutoka kwa denominator ili niweze kukusaidia kulitatua. Tuma swali linalofuata 📸