题干

如图,在直角坐标系 xoy 中,已知点 A(2,0),B(1,3), 直线 x=t(0<t<2) ,将 ΔABC 分成两部分,记左侧部分的多边形为 Ω ,设 Ω 各边的平方和为 f(t) , Ω 各边长的倒数和为 g(t)  .
 
(Ⅰ)求分别求函数 f(t) 和 g(t) 的解析式;  
(Ⅱ)是否存在区间 (a,b) ,使得函数 f(t) 和 g(t) 在该区间上均单调递减?若存在,求 b−a 的最大值;若不存在,说明理由.
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答案(点此获取答案解析)

解:(Ⅰ)当 0<t≤1 时,多边形 Ω 是三角形(如图①),边长依次为t,

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    While serious training is important for all dogs, playtime is just as important. ____ Use these games to help teach your dog how to play.

1). Hide and Seek

    Hide and seek isn't just for kids. Dogs can really enjoy this game. Pick up one of your dog's favorite toys or treats. Tell your dog to stay. ____ When you are ready, call your dog to come to you. If possible, squeak (使吱吱叫) the toy or shake the treats. Reward your dog with praise and the toy or treat when she finds you.

2). Fetch

    Many dogs have a natural ability to fetch. Other dogs can be taught how. ____ Play indoors with a soft toy or outdoors in a fenced-in area with a ball or disc. For dogs that really love to run, try this game of fetch!

3). Find the Treat

    Dogs have superior senses of smell, and most love to use their noses to find food. Let your dog use her brain and her nose to find hidden goodies. First, have your dog stay out of sight. Then, hide her favorite treats in various places around the room. ____ If help is needed, you can lead her around or point to areas for her to explore.

Whatever the game, safety comes first! Remember to watch your dog for signs of exhaustion or overheating when you are playing. Stop if your dog seems tired or shows signs of anxiety. ____ When other dogs or people are around, it may create a dangerous distraction.

A. Then, go to find a good hiding place.

B. Try different games to see which your dog responds to best.

C. A good game of fetch can be played almost anywhere.

D. You can include games in training as well.

E. Also be aware of your surroundings when playing with your dog.

F. Encourage your dog to play with other dogs.

G. Bring your dog back in and tell her to “go find!”