Cho hình chóp \(S. A B C\) với \(M, N, P\) lần lượt là trung điểm các cạnh \(B C, A C, A B\) và thỏa mãn: \(S M=N P, S N=M P, S P=M N\).
Tỉ số \(\frac{\mathrm{dt}^{2}(S A B)+\mathrm{dt}^{2}(S A C)+\mathrm{dt}^{2}(S B C)}{\mathrm{dt}^{2}(M N P)}\) bằng bao nhiêu?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
\(d t^{2} S A C+d t^{2} S B C+d t^{2} S A B\)
\(=\frac{1}{4}\left(S A^{2} \cdot S C^{2}+S B^{2} \cdot S C^{2}+A B^{2} \cdot S I^{2}\right)\)
\(=\frac{1}{4}\left[S C^{2} \cdot\left(S A^{2}+S B^{2}\right)+A B^{2} \cdot S I^{2}\right]=\frac{1}{4}\left(S C^{2} \cdot A B^{2}+A B^{2} \cdot S I^{2}\right)\)
\(=\frac{1}{4} A B^{2} \cdot\left(S C^{2}+S I^{2}\right)=\frac{1}{4} A B^{2} \cdot C I^{2}=\mathrm{dt}^{2} \mathrm{ABC}\).
Mặt khác, dễ thấy \(\mathrm{dt}^{2} \mathrm{ABC}=16. \mathrm{dt}^{2} \mathrm{MNP}\).
Do đó \(\frac{\left(\mathrm{dt}^{2} \mathrm{SAB}+\mathrm{dt}^{2} \mathrm{SAC}+\mathrm{dt}^{2} \mathrm{SBC}\right)}{\mathrm{dt}^{2} \mathrm{MNP}}=16\).
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Câu hỏi liên quan
Find the word which has a different sound in the part underlined.
“Về quan hệ giữa đổi mới kinh tế và đổi mới chính trị, phải tập trung làm tốt đổi mới kinh tế, đáp ứng những đòi hỏi cấp bách của nhân dân về đời sống, việc làm và các nhu cầu xã hội khác, xây dựng cơ sở vật chất – kĩ thuật của chủ nghĩa xã hội, coi đó là điều kiện quan trọng để tiến hành thuận lợi đổi mới trong lĩnh vực chính trị. Đồng thời đổi mới kinh tế phải từng bước đổi mới tổ chức và phương thức hoạt động của hệ thống chính trị, phát huy ngày càng tốt quyền làm chủ và năng lực sáng tạo của nhân dân trên các lĩnh vực chính trị, kinh tế, văn hóa, xã hội”.
(Đảng Cộng sản Việt Nam, Văn kiện Đại hội đại biểu toàn quốc lần thứ VII, NXB Sự thật, Hà Nội, 1991, tr.54)
Đổi mới kinh tế được coi là điều kiện quan trọng và phải
Những thiết bị nào sau là thiết bị số?
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Read the following passage about the The Importance of Social Media in Modern Society and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
In the 21st century, social media has become a crucial element of everyday life[I]. Platforms such as Facebook, Twitter, Instagram, and TikTok link individuals around the world, [IV]. Although some may critique social media for promoting negativity, it is important to acknowledge its numerous positive effects on society[III]. This essay will delve into the importance of social media, its influence on shaping public perception, and the challenges it poses.[II]
One of the primary benefits of social media is its ability to foster communication and connection. People can maintain relationships with friends and family, regardless of geographical barriers. This aspect is particularly vital for those who live far away from loved ones. For example, a student studying abroad can easily share their experiences with family through posts, photos, and video calls. Furthermore, social media enables individuals to connect with like-minded people and build communities around shared interests or causes. Activist groups, for instance, often use social media platforms to rally support for important issues, raising awareness and mobilizing action more efficiently than traditional methods.
Moreover, social media serves as a powerful tool for information dissemination. News spreads rapidly through these platforms, allowing individuals to stay informed about current events. During emergencies, such as natural disasters, social media can provide crucial information in real time, helping people stay safe and informed. However, this rapid dissemination of information also raises concerns about the accuracy and reliability of the content being shared. Misinformation can spread just as quickly as legitimate news, leading to confusion and mistrust.
Despite the challenges posed by misinformation, social media plays a significant role in shaping public opinion. People often turn to these platforms to voice their opinions and engage in discussions on various topics. For instance, political debates and social movements frequently gain traction through social media, allowing individuals to express their views and influence others. This democratization of discourse can empower marginalized voices and facilitate social change. However, it is crucial to approach online discussions critically, as echo chambers can form, reinforcing existing beliefs rather than encouraging open dialogue.
In conclusion, while social media presents challenges such as misinformation and polarized discussions, its positive contributions to communication, information dissemination, and social activism cannot be overlooked. As society continues to evolve, it is essential to harness the potential of social media while being mindful of its pitfalls. By promoting responsible use and critical thinking, we can maximize the benefits of social media and foster a more connected and informed society.
Which of the following best summarises the passage?
Cho ba tập hợp \({{C}_{\mathbb{R}}}M=\left( -\infty ;3 \right),\,{{C}_{\mathbb{R}}}N=\left( -\infty ;-3 \right)\cup \left( 3;+\infty \right)\) và \({{C}_{\mathbb{R}}}P=\left( -2;3 \right]\).
Một công ty cần xây một cái kho chứa hàng dạng hình hộp chữ nhật có thể tích \(2000 \mathrm{~m}^{3}\) bằng vật liệu gạch và xi măng, đáy là hình chữ nhật có chiều dài bằng hai lần chiều rộng. Người ta cần tính toán sao cho chi phí xây dựng thấp nhất, biết giá vật liệu xây dựng là \(500.000~ đồng /\mathrm{m}^{2}\). Khi đó, chi phí thấp nhất gần với số nào nhất trong các số dưới đây?
Mark the letter A, B, C or D on your answer sheet to indicate the best arrangement of utterances or sentences to make a meaningful exchange or text in each of the following questions from 13 to 17.
Hi Sarah,
a. I'm really looking forward to joining the cooking class you recommended.
b. Also, I appreciate the recipe you sent me; it looks delicious!
c. However, I'm quite busy this month, so I might not be able to attend all the sessions.
d. Thanks for your help in finding that class — it sounds perfect for me.
e. Let’s try to cook together sometime, that would be fun!
Write back soon.
James
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Các thiết bị âm thanh số cần có mạch điện tử DAC để làm gì?
Công thức liên hệ giữa tốc độ dài, tốc độ góc với chu kì T và tần số f cho bởi
Trong các thí nghiệm sau thí nghiệm nào không phải là phép thử ngẫu nhiên:
Read the following passage about managing change and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Growing up in Athens, Greece, Lydia Borsi remembers feeling tested when she tried to deal with mental health issues. Borsi says she had been seeing a therapist for anxiety. But she notes that people in Greece do not openly discuss mental health issues, which also get little attention in general healthcare services. “It was a lot more secretive. And people thought that I was a lot more unique,” Borsi said.
That all changed in 2017 when she moved to the United States to study at the University of Rochester in Rochester, New York. “When I came here, I really liked that people were not afraid to speak up about mental health and say that it’s important,” she said. The university was very supportive of her needs and offered plenty of information. She also became involved with a school group called Active Minds that helps students deal with mental health issues. [A]
Then due to the spread of the novel coronavirus, the University of Rochester had to move all its classes and some of its mental health resources online. Luckily, Borsi was able to connect with a mental health expert outside the school, in the local community. [B]
But as many of her American friends returned home, Borsi was stuck. Greece had succeeded in limiting the spread of the virus within its borders, but flights there from the U.S. are barred until July. Also, the health crisis has put her plans to seek admission to medical school in Britain on hold. [C] And she is not alone.
[D] In April, Active Minds launched a survey of over 2,000 students at U.S. colleges and universities. The study found that over 80 percent of those asked said the coronavirus crisis had negatively affected their mental health. One in five said it has affected them severely.
Laura Horne, chief program officer at Active Minds, says the findings are especially troubling given that the crisis is only going to make it harder for colleges and universities to help these students. “Colleges and universities had to pivot rather quickly to respond to COVID-19 and figure out all facets of university life, including mental health services. Now they have to figure out how to communicate with students,” Horne said.
Frank Chen is a Houston, Texas-based psychiatrist who has worked with college-age young adults. He points out that individuals at that age are in an important stage of their mental development. And college can be a difficult experience for students with or without mental health issues, as they balance work, studies, and personal relationships. Adding a major world event, like the spread of the coronavirus, makes it very difficult to predict what the long-term psychological effects might be. “I don’t think that there’s another event in the history of the people who are alive now that can really measure up to this,” said Chen.
What did Borsi enjoy when she came to the United States?
Người ta tạo ra thuốc trừ sâu sinh học có chứa virut ...... Khi màng keo tan ra, virut hoạt động và gây chết cho sâu. Điền vào chỗ trống (......) từ hoặc cụm từ nào dưới đây cho câu trên đúng nghĩa?
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Discover the Future of Dining at Viet Organic Garden Restaurant!
At Viet Organic Garden Restaurant, we offer a (7)______of fresh, organic dishes designed to meet the growing demands of modern consumers. As the world experiences a (8)_______toward healthier, eco-friendly lifestyles, we are proud to provide a dining experience that prioritizes sustainability and wellness.
Unlike the other restaurants that depend on processed foods, we source our ingredients directly from local farmers. This ensures that our supply is never (9)______and allows us to deliver meals rich in flavor and nutrition. (10)______ ethical sourcing and environmentally friendly practices, we bring quality and care to every plate.
When you place your (11)______at Viet Organic Garden Restaurant, you can trust that each dish is made with love and care. Join us and be part of this exciting movement. Whether you're looking for a cozy weekend meal or a refreshing take on dining, Viet Organic Garden Restaurant stands apart from the (12)______ options in the market as a leader in sustainable and healthy dining.
Each of the following sentences has one error (A, B, C or D). Find it and blacken your choice on your answer sheet.
The students in the class were excited about the project, but she didn’t know how to start it.
Yếu tố nào sau đây ảnh hưởng đến văn minh Đông Nam Á (từ trước Công nguyên đến thế kỉ VII)?
Việc hình thành các chuỗi đô thị ven biển, đô thị hải đảo có ý nghĩa
Choose A, B, C or D:
John was in Hanoi and wanted to send a parcel to his parents. He asked a local passer-by the way to the post-office.
- John: “Can you show me the way to the nearest post office, please?”
- Passer-by: “______”.
