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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You're on a roll — Here are the solutions to the problems: 10. Omuando borrows KSh 90,000 for 5 years at 6 (1)/(2)\% simple interest p.a. What amount does he have to pay at the end of that time? Step 1: Identify the given values. Principal (P) = KSh 90,000 Time (T) = 5 years Rate (R) = 6 (1)/(2)\% p.a. = 6.5\% = (6.5)/(100) = 0.065 Step 2: Calculate the simple interest (SI). The formula for simple interest is SI = P × R × T. SI = 90000 KSh × 0.065 × 5 SI = 90000 × 0.325 SI = 29250 KSh Step 3: Calculate the total amount to be paid. The total amount (A) is the principal plus the simple interest. A = P + SI A = 90000 KSh + 29250 KSh A = 119250 KSh The total amount Omuando has to pay is 119250 KSh. 11. Solve for x in the equation, 9^x+1 + 3^2x = 270 Step 1: Express all terms with the same base. The base 3 can be used since 9 = 3^2. Rewrite 9^x+1 as (3^2)^x+1. (3^2)^x+1 + 3^2x = 270 3^2(x+1) + 3^2x = 270 3^2x+2 + 3^2x = 270 Step 2: Factor out the common term 3^2x. 3^2x · 3^2 + 3^2x = 270 3^2x(3^2 + 1) = 270 3^2x(9 + 1) = 270 3^2x(10) = 270 Step 3: Isolate the exponential term. 3^2x = (270)/(10) 3^2x = 27 Step 4: Express the right side with the same base as the left side. Since 27 = 3^3: 3^2x = 3^3 Step 5: Equate the exponents and solve for x. 2x = 3 x = (3)/(2) The value of x is (3)/(2). Got more? Send 'em!