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Question

Trong hệ trục tọa độ oxyz cho tam giác abc vuông tại a có a thuộc tia ox thuộc tia oy và trọng tâm tam giác ABC thuộc tia oz tính tỉ số OA/OB

Thought

Clarifying point locations

I’m mapping out triangle ABC's vertices: A on ray Ox and B on ray Oy, with O as the origin. This setup clarifies the coordinates and their relationship for further analysis.

Evaluating perpendicularity

I'm examining B as (-a, b, 0) and C as (-a, -b, z_C). Their orthogonality reveals specific insights into the triangle configuration and coordinates.

Thought about tỷ số OA/OB cho 4 giây

Answer

Giả sử hệ trục tọa độ OxyzOxyz với OO là gốc tọa độ. Theo giả thiết:

  • Tam giác ABCABC vuông tại AA.
  • Điểm AA nằm trên tia OxOx, nên ta có tọa độ A=(a,0,0)A = (a,0,0) với a>0a > 0.
  • Điểm BB nằm trên tia OyOy, nên B=(0,b,0)B = (0,b,0) với b>0b > 0.
  • Trọng tâm GG của tam giác ABCABC thuộc tia OzOz, nghĩa là tọa độ của GG có dạng (0,0,zG)(0,0,z_G) với zG>0z_G > 0.

Vì GG là trọng tâm nên:

G=(xA+xB+xC3, yA+yB+yC3, zA+zB+zC3).G = \left(\frac{x_A+x_B+x_C}{3},\,\frac{y_A+y_B+y_C}{3},\,\frac{z_A+z_B+z_C}{3}\right).

Thay tọa độ ta có:

G=(a+0+xC3, 0+b+yC3, 0+0+zC3)=(a+xC3, b+yC3, zC3).G = \left(\frac{a+0+x_C}{3},\,\frac{0+b+y_C}{3},\,\frac{0+0+z_C}{3}\right) = \left(\frac{a+x_C}{3},\,\frac{b+y_C}{3},\,\frac{z_C}{3}\right).

Do GG nằm trên OzOz, nên hoành độ và tung độ của GG bằng 0:

a+xC3=0⇒xC=−a,\frac{a+x_C}{3} = 0 \quad \Rightarrow \quad x_C = -a, b+yC3=0⇒yC=−b.\frac{b+y_C}{3} = 0 \quad \Rightarrow \quad y_C = -b.

Vậy C=(−a,−b,zC)C = (-a,-b,z_C) với zCz_C là một số thực chưa xác định.

Tiếp theo, tam giác ABCABC vuông tại AA nên:

AB→⋅AC→=0.\overrightarrow{AB} \cdot \overrightarrow{AC} = 0.

Tính các véc-tơ:

AB→=B−A=(0−a,  b−0,  0−0)=(−a,  b,  0),\overrightarrow{AB} = B - A = (0 - a,\; b - 0,\; 0 - 0) = (-a,\; b,\; 0), AC→=C−A=(−a−a,  −b−0,  zC−0)=(−2a,  −b,  zC).\overrightarrow{AC} = C - A = (-a - a,\; -b - 0,\; z_C - 0) = (-2a,\; -b,\; z_C).

Tích vô hướng:

AB→⋅AC→=(−a)(−2a)+(b)(−b)+(0)(zC)=2a2−b2.\overrightarrow{AB} \cdot \overrightarrow{AC} = (-a)(-2a) + (b)(-b) + (0)(z_C) = 2a^2 - b^2.

Điều kiện vuông tại AA cho ta:

2a2−b2=0⇒b2=2a2⇒b=a2  (với b>0).2a^2 - b^2 = 0 \quad \Rightarrow \quad b^2 = 2a^2 \quad \Rightarrow \quad b = a\sqrt2 \;(\text{với } b > 0).

Cuối cùng, độ dài OA=aOA = a và OB=b=a2OB = b = a\sqrt2.

Tỉ số cần tìm:

OAOB=aa2=12.\frac{OA}{OB} = \frac{a}{a\sqrt2} = \frac{1}{\sqrt2}.

Question

Viết một bài báo cáo khoảng 180 đến 200 từ về những lợi ích và bất lợi của robot làm việc nhà bằng tiếng Anh

Thought

Suy nghĩ cho 1 giây

Answer

Benefits and Drawbacks of Household Robots

Household robots have increasingly become a staple in modern homes, offering a range of benefits that enhance daily living. One significant advantage is the automation of mundane tasks such as cleaning, cooking, and lawn maintenance. This automation not only saves time but also allows individuals to focus on more meaningful activities or work. Additionally, robots equipped with smart technology can improve efficiency through precise and consistent performance, reducing the likelihood of human error. For families with elderly members or individuals with disabilities, household robots provide invaluable assistance, promoting independence and safety.

However, the integration of robots into home environments also presents certain drawbacks. The initial cost of purchasing and maintaining advanced robotic systems can be prohibitive for many households. Moreover, there is a learning curve associated with operating these devices, which may deter some users. Privacy concerns arise as robots often rely on data collection and internet connectivity, potentially exposing personal information to security risks. Additionally, the reliance on robots for everyday tasks might lead to a decrease in human interaction and physical activity, impacting social skills and overall health.

In conclusion, while household robots offer significant benefits in terms of efficiency, convenience, and support, it is essential to consider the associated costs, privacy issues, and potential impacts on human behavior. Balancing these factors will determine the extent to which robots can be effectively and sustainably integrated into our homes.

Question

Viết ngắn gọn hơn

Thought

Rút ngắn nội dung

Đang làm việc chỉnh sửa báo cáo, tôi nhận thấy nội dung có thể ngắn gọn hơn để phù hợp với yêu cầu.

Suy nghĩ cho trong giây lát

Answer

Benefits and Drawbacks of Household Robots

Household robots offer numerous advantages that enhance daily life. They automate tasks like cleaning, cooking, and lawn care, saving time and allowing people to focus on more important activities. Smart robots can perform tasks consistently and efficiently, reducing errors. For families with elderly members or individuals with disabilities, these robots provide essential assistance, promoting independence and safety.

However, there are also disadvantages to consider. The initial cost of purchasing and maintaining household robots can be high, making them inaccessible for some families. Operating these devices may require technical knowledge, which can be a barrier for some users. Privacy concerns arise as robots often collect data and connect to the internet, posing potential security risks. Additionally, excessive reliance on robots for daily tasks might reduce physical activity and human interaction, potentially impacting health and social skills.

In summary, while household robots offer significant benefits in terms of efficiency and support, it is important to address the costs, privacy issues, and possible effects on human behavior to ensure their effective integration into homes.

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