"破罐子破摔“用英语怎么说?

Smash a pot to pieces just because it's cracked -- write oneself off as hopeless and act recklessly

throw the helve after the hatchet

Dear Xiao Hong,
How are you?I’m sorry to know you failed in your lessons many times.I believe you are a smart student.Don’t worry about it.Remember:Failure is the mother of success.Maybe you should tell your parents and they can help you.Now I will tell you something about how to study well.I hope it will help you.First you should work hard in class,listen carefully,use your head,ask and answer questions,work with your partners,do your homework carefully and so on.Second you should do more exercises.Third it is good to build self-confidence in everything.
Well,I’ll stop here.Good luck!
Yours,
Mr.Liu

用沉没成本的概念?沉沉成本意为已经投入并且无法收回的成本.关于“沉淀成本”有许多生活中的事例可以说明,比如说你花了20元去看一场电影,15分钟之后,你觉得这是一部你所无法忍受的粗制滥造的影片.那么你是继续看下去,一直到2个小时之后影片结束呢?还是立即离开电影院去图书馆查资料?如果你心疼那20元门票,而坚持把电影看完,那么除了已经支出的20元沉淀成本（电影院当然不会因你认为影片质量太差而退钱给你）之外,你还付出了2个多小时的宝贵时间成本.这就是破罐子破摔的表现.

罐子已经破了,所以就无所谓了,用不着小心对待了,可以随便摔.破天荒就是开荒,原来是荒地被开肯出来,那肯定是从来没有过、没有第二份的意思了.

pò guàn pò shuāi
成语：破罐破摔
【解释】：把破损的罐子摔破.比喻有了缺点、错误不改正,反而有意向更坏的方向发展.
【示例】：好些年来,他自轻自贱,成了习惯,破罐子破摔,不想学好了.（周立波《暴风骤雨》第二部第十七章）
【语法】：联合式；作谓语、定语、宾语；含贬义