This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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Okay, I will solve both questions in English. Question 5: Given: First term (a) = 4 Last term (l) = 20 Sum of terms (S_n) = 252 We need to calculate the number of terms (n) and the common difference (d). Step 1: Find the number of terms (n) using the formula for the sum of an arithmetic progression. The sum formula is S_n = (n)/(2)(a + l). 252 = (n)/(2)(4 + 20) 252 = (n)/(2)(24) 252 = 12n Divide both sides by 12: n = (252)/(12) n = 21 The number of terms is 21. Step 2: Find the common difference (d) using the formula for the last term. The formula for the last term is l = a + (n-1)d. 20 = 4 + (21-1)d 20 = 4 + 20d Subtract 4 from both sides: 20 - 4 = 20d 16 = 20d Divide both sides by 20: d = (16)/(20) Simplify the fraction: d = (4)/(5) The common difference is (4)/(5) or 0.8. Question 6: Given: Initial number of bacteria (P_0) = 2500 The number increases by 60% every 20 minutes. Target number (P_t) = 16384 bacteria We need to find out how long it will take to reach the target number. Step 1: Determine the growth factor and set up the formula. The growth factor per 20-minute period is 1 + 0.60 = 1.6. The exponential growth formula is P_t = P_0 × (growth factor)^k, where k is the number of 20-minute periods. 16384 = 2500 × (1.6)^k Step 2: Solve for k. Divide both sides by 2500: (16384)/(2500) = (1.6)^k 6.5536 = (1.6)^k To find k, we can test powers of 1.6: 1.6^1 = 1.6 1.6^2 = 2.56 1.6^3 = 4.096 1.6^4 = 6.5536 Thus, k = 4. Step 3: Calculate the total time. Since k is the number of 20-minute periods, the total time is k × 20 minutes. Time = 4 × 20 = 80 minutes. It will take 80 minutes to reach 16384 bacteria. That's 2 down. 3 left today — send the next one.