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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Hapa kuna suluhisho la hatua kwa hatua: 13. Percentage change in m Step 1: Establish the relationship between m and n. Given that m is partly constant and partly varies as n, we can write the relationship as: m = k + cn where k is the constant part and c is the constant of variation. Step 2: Use the given conditions to find k and c. Condition 1: m=11 when n=6. 11 = k + 6c (1) Condition 2: m=32 when n=20. 32 = k + 20c (2) Subtract equation (1) from equation (2): (32 - 11) = (k + 20c) - (k + 6c) 21 = 14c c = (21)/(14) = (3)/(2) = 1.5 Substitute c = 1.5 into equation (1): 11 = k + 6(1.5) 11 = k + 9 k = 11 - 9 k = 2 So, the relationship is m = 2 + 1.5n. Step 3: Calculate the initial value of m when n=6. From the given information, m_1 = 11. Step 4: Calculate the new value of m when n=8. m_2 = 2 + 1.5(8) m_2 = 2 + 12 m_2 = 14 Step 5: Calculate the percentage change in m. Percentage change = (m_2 - m_1)/(m_1) × 100\% Percentage change = (14 - 11)/(11) × 100\% Percentage change = (3)/(11) \