Phi

🔍

question:If ( x=frac{2-isqrt{3}}{3} ) where ( i=sqrt{-1} ), then ( frac{1}{x^2-x} ) is equal to? **A)** (frac{9}{13} + frac{18isqrt{3}}{13}) **B)** (frac{9}{13} - frac{18isqrt{3}}{13}) **C)** (frac{18 - 9isqrt{3}}{13}) **D)** (frac{18 + 9isqrt{3}}{13}) **E)** (frac{9 + 18}{13})

answer:1. **Calculate ( x^2 )**: [ x^2 = left(frac{2-isqrt{3}}{3}right)^2 = frac{(2-isqrt{3})^2}{9} = frac{4 - 4isqrt{3} + 3}{9} = frac{7 - 4isqrt{3}}{9} ] Simplifying further: [ x^2 = frac{7}{9} - frac{4}{9}isqrt{3} ] 2. **Calculate ( x^2 - x )**: [ x^2 - x = left(frac{7}{9} - frac{4}{9}isqrt{3}right) - left(frac{2}{3} - frac{1}{3}isqrt{3}right) = frac{7 - 4isqrt{3} - 6 + 2isqrt{3}}{9} = frac{1 - 2isqrt{3}}{9} ] 3. **Calculate ( frac{1}{x^2-x} )**: [ frac{1}{x^2 - x} = frac{1}{frac{1 - 2isqrt{3}}{9}} = frac{9}{1 - 2isqrt{3}} = frac{9(1 + 2isqrt{3})}{1 - (-4 times 3)} = frac{9 + 18isqrt{3}}{13} ] # Conclusion: The solution for ( frac{1}{x^2-x} ) is ( frac{9 + 18isqrt{3}{13}} ). The final answer is boxed{**Provide A)** (frac{9}{13} + frac{18isqrt{3}}{13})}

question:Instructions: You are shown a conversation between a user and system. Identify who has spoken the indicated sentence based on the conversation. Input: Sentence1: Hi I need to book a guesthouse with free wifi in Cambridge please Sentence2: I would like one in the moderate price range. Sentence3: Anywhere in town, need two rooms for three people for 5 nights beginning on Monday next week. Can you give me a confirmation number as well, please? Sentence4: The postcode is cb21tt. Is there anything else I can help you with? Sentence5: I have the a and b guesthouse in the east that is a 4 star moderatly price guesthouse. Would you like to make reservations? Sentence6: That is everything, you were so helpful. Sentence7: I'm also looking for an attraction to go to in the centre. Do you have any recommendations? Sentence8: You're welcome, glad I could help. Sentence9: i have successfully booked. Reference number is : 7PPQG9Q1 Sentence10: Yes, I would suggest the old schools. Sentence11: Yes. I need it for three for five nights starting from Monday on. Sentence12: Great, I have several options for you. Is there an area of town you prefer? Sentence13: Excellent. What's the postcode? Sentence14: Did you have a price range in mind, or a particular section of the city? Question: Who has spoken the sentence 7? (A) User (B) System Output:

answer:A

question:Alex, I'm extremely disappointed to see that you've missed the deadline for the article on inflammatory bowel disease. This is not the first time, and it's causing significant issues for our project. The entire team is now behind schedule, and we're at risk of missing the conference submission deadline. Perhaps you should focus more on your deadlines and less on your creative flair. Your lack of attention to detail is concerning, and it's starting to affect our credibility. If this happens again, I'll have to reconsider our collaboration. Best regards, Dr. Emily Clarke

answer:Hi Alex, I hope you're doing well. I wanted to touch base with you about the article on inflammatory bowel disease. I noticed that we missed the deadline, and this isn't the first time it's happened. It's really important for us to stay on schedule, as it affects the whole team and puts us at risk of missing the conference submission deadline. I understand that you bring a lot of creativity to our projects, but it's crucial that we also maintain a focus on meeting our deadlines. Your attention to detail is so important, and I believe you can balance both creativity and timeliness. Let's work together to ensure this doesn't happen again. If you're facing any challenges or need support, please let me know. I'm here to help. Best, Emily

question:What is the reversed form of the string 'algorithm'?

answer:<tool_call>[{name: reverse_string, arguments: {text: algorithm}}]</tool_call>