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唔識做功課23

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我連條題目都睇唔明! solve quadratic equations1. A hall contains 216 seats. If the number of seats in each row is 6 more than the total number of rows of seats, how many rows of seats are there in the hall?2. The Gateway Arch in the USA is 192 m tall. A ball initially at the rest is dropped from the top of the Gateway... 顯示更多我連條題目都睇唔明! solve quadratic equations 1. A hall contains 216 seats. If the number of seats in each row is 6 more than the total number of rows of seats, how many rows of seats are there in the hall? 2. The Gateway Arch in the USA is 192 m tall. A ball initially at the rest is dropped from the top of the Gateway Arch. The distance (h m) that it falls t seconds is given by h=5t^2. Find the time taken by the ball to reach the ground. (give the answer correct to 2 decimal places.) 更新: 3. A wire of length 20 cm is bent to form a rectangle. Can the area of the rectangle be 26 cm square?

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圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif 哈哈哈，呢個《唔識做功課》系列係暑假都繼續：「我連條題目都睇唔明!」為左令你學習得更好，今次要詳盡ｄ講解一下！ 1. A hall contains 216 seats. If the number of seats in each row is 6 more than the total number of rows of seats, how many rows of seats are there in the hall? 一個禮堂共有 216 個座位。若每一行的座位數比總行數多 6 ，問禮堂共有多少行座位。 Let n be the number of rows of seats in the hall. Each row contains n + 6 seats. n(n + 6) = 216 n2 + 6n - 216 = 0 (n - 12)(n + 18) = 0 n = 12 or n = -18 (rejected) Therefore, there are 12 rows of seats in the hall. 2. The Gateway Arch in the USA is 192 m tall. A ball initially at the rest is dropped from the top of the Gateway Arch. The distance (h m) that it falls t seconds is given by h = 5t2. Find the time taken by the ball to reach the ground. (give the answer correct to 2 decimal places.) 美國的聖路易斯拱門高 192 米。一個原本靜止的球從拱門頂掉下來。球在掉下 t 秒後所跌的距離是 h 米，其中 h = 5t2。問球到達地面的所需時間。（答案取至小數後兩個位。） Consider h = 192. h = 5t2 192 = 5t2 t2 = 38.4 t = √38.4 or t = -√38.4 (rejected) t = 6.196773354 The required time is 6.20 s (correct to 2 d.p.) 2014-08-13 19:36:18 補充： 3. A wire of length 20 cm is bent to form a rectangle. Can the area of the rectangle be 26 cm square? 一條長 20 cm 的電線屈曲成一個長方形，問這個長方形的面積能否是 26 cm2？ 2014-08-13 19:37:23 補充： Let the length of the rectangle be x cm. The width is then (20/2 - x) = (10 - x) cm. The area (in cm2) is x(10 - x) = 10x - x2 = -(x2 - 10x) = -(x2 - 10x + 25 - 25) = -(x2 - 10x + 25) + 25 = -(x - 5)2 + 25 ≤ 25 The maximum area is 25 cm2. Thus, the area cannot be 26 cm2. 2014-08-13 19:57:48 補充：呢個係叫 completing the square (配方法) 即是弄一個完全平方 (perfect square) 出來。善用 a2 + 2ab + b2 = (a + b)2 的道理。當我們見到 x2 + ax 的時候，可以故意這樣寫： x2 + ax + (a/2)2 - (a/2)2 = x2 + 2(a/2)x + (a/2)2 - (a/2)2 = (x + a/2)2 - (a/2)2 = (x + a/2)2 - a2/4 明白嗎？ 2014-08-13 20:13:54 補充： ╭∧---∧╮ │ .??? │ ╰/) ? (\╯ 這個方法是用處是判斷二次函數 (quadratic function) 的最大 (maximum) 或最小 (minimum) 值，所以在數學上是有用的。例如： x2 + 6x + 8 = (x + 2)(x + 4) 要懂得 factorize = x2 + 6x + 9 - 1 = (x + 3)2 - 1 也要懂得 complete the square ≥ 0 - 1 = -1 即 minimum of x2 + 6x + 8 is -1.