题目

等腰梯形ABCD的两底分别为AD=2a，BC=a，∠BAD=45°，作直线MN⊥AD交AD于M，交折线ABCD于N，记AM=x,试将梯形ABCD位于直线MN左侧的面积y表示为x的函数，并写出函数的定义域. 答案：y= 解析:作BH⊥AD，H为垂足，CG⊥AD，G为垂足， 依题意，则有AH=，AG=a. 当M位于点H的左侧时, N∈AB， 由于AM=x，∠BAD=45°. ∴MN=x. ∴y=S△AMN=x2（0≤x≤）. （2）当M位于HG之间时， 由于AM=x， ∴MN=，BN=x-. ∴y=S直角梯形AMNB=［x+（x-）］=ax- （3）当M位于点G的右侧时， 由于AM=x，MN=MD=2a-x. ∴y=S梯形ABCD-S△MDN = 综上：yRecently I experienced a wonderful lesson in how little things still mean a lot. I live on the Island of Hawaii. About a month ago, when I    36   my car and was about to drive off, I glanced down at the roadside. A piece of paper   37  my eye. I picked it up and read it   38  . Instantly I was grateful that I had done that. The form   39  to be a receipt from the State Motor Vehicle Division, documenting the owners’   40   of their Vehicle’s Registration fees. Quickly I put myself in their   41  and figured: no one would throw this away, especially if it was current. I also  42  the form for contact or any   43  data, perhaps a license tag(牌照) or telephone number. But that seemed   44  . Although the form had been   45  on the wind, where in the busy, crowded parking lot would I find the   46  ? So I checked the date and    47  the names of the owners, who must be in our town. I believed that the best and easiest step to  48  was to put the form in a(n)   49  addressed to the couple and mail it by post. Further, I imagined how frantic (狂乱的) I’d be   50   I had misplaced the receipt. It is much easier to make a(n)   51  to return it than to leave them angry, upset etc. over the  52  , so I did as I thought. My hunch(预感) was right. On the weekend a happy couple called  53  my house and brought me a big gift. They said they had panicked and searched for the receipt  54    everywhere before giving up. Without it they would lose $8,000. It felt great to know I’d helped someone avoid a major trouble by doing   55  that at first glance seemed minor. 36. A. parked                     B. bought                    C. started                    D. found 37. A. blocked                    B. caught                    C. kept                        D. covered 38. A. suddenly                  B. carefully                  C. gladly                     D. b riefly 39. A. came out                 B. worked out              C. turned out                     D. gave out   40. A. permission        B. plan                        C. care                        D. payment 41. A. side                         B. shoes                            C. place                      D. position 42. A. held up                    B. knocked over          C. kept up                   D. looked over 43. A. personal                  B. secret                            C. public                     D. open 44. A. important                 B. possible                  C. impractical              D. useful 45. A. born                         B. played                    C. fetched                   D. grown 46. A. hosts                       B. guests                    C. partners                 D. owners 47. A. recalled                   B. noted                      C. called                     D. changed 48. A. set                           B. make                      C. take                        D. do 49. A. envelope                 B. pocket                    C. bag                         D. dustbin 50. A. as                            B. if                      C. though                    D. since 51. A. attempt                    B. experiment              C. promise                  D. request 52. A. pain                         B. luck                         C. loss                        D. mistake 53. A. on                            B. at                            C. to                            D. in 54. A. violently                   B. severely                  C. angrily                    D. madly 55. A. anything                  B. nothing                   C. everything              D. Something