DevlikamovMath/English

В прямоугольном треугольнике высота и медиана, проведенные из прямого угла делят этот угол на три равные части. Площадь треугольника, образуемого вершиной прямого угла и точками пересечения высоты и медианы с гипотенузой, равна 2sqrt3. Найдите плошадь круга, вписанного в исходный треугольник.

Вот и наступил день X, когда наши пути с Мухаммадбеком начинают расходиться. Мухаммадбек — один из моих самых преданных учеников, который был со мной на протяжении трёх лет: с 8 класса до середины первого курса лицея. За это время он изменился не только физически, но и интеллектуально, успешно освоив полный курс математики за 11 классов. Вместе мы прошли большой путь: поступили в академический лицей, решив 19 из 20 задач в секции математики, а также Мухаммадбек достойно сдал экзамен SAT, набрав 780 из 800 баллов по математике. На нашем пути были и трудности, и разногласия, но, думаю, светлых и радостных моментов было гораздо больше. Мы многому научились друг у друга, и для меня было искренним удовольствием работать вместе. В добрый путь! Я верю, что вы добьётесь больших высот в своей жизни 🙌🏻 This is the day when my path and Muhammadbek’s begin to part. He is one of my most dedicated students, who has been with me for the past three years — from the 8th grade to the middle of his first year at academic lyceum. During this time, Muhammadbek has grown not only physically, but also intellectually, having completed the full high school mathematics curriculum. Together, we achieved a lot: we gained admission to an academic lyceum by solving 19 out of 20 problems in the math section, and he also successfully passed the SAT, scoring an impressive 780 out of 800 in Math. Our journey was not without its challenges — there were disagreements as well as many positive moments, and I believe the latter prevailed. We learned a great deal from each other, and it has truly been a pleasure working together. I wish you all the best on your journey ahead. I truly believe you will achieve great things in life 🙌🏻

Let’s cook 🙏

People will blame fate, gods, and the world—anything but themselves

“Not for nothing” There is a good reason for something.Something happened / is true because it is justified by facts or results 🤨 In other words: it wasn’t pointless, accidental, or without cause It’s very close to: • “for a reason” (more neutral) • “не зря” (your original Russian idea) 🔥Important nuance: It often implies: • experience • reputation • warning • or a result that proves something So it’s not just “reason” — it’s usually a justified reason 🌀How to use it 🌀 ☀️A. General statements (very common) • It’s not for nothing that she got promoted so quickly. • It’s not for nothing that this university is so famous. ☀️ About reputation / opinions • He’s not called a genius for nothing. • There’s a reason people respect him — not for nothing. ☀️Personal experience • Not for nothing did I spend years practicing. It all paid off. • I didn’t go through all that for nothing. ☀️Warnings / logic • Not for nothing do people say you should double-check your work. 🔠Most common pattern🔠 It’s not for nothing that + clause • It’s not for nothing that he succeeded. • It’s not for nothing that people trust her. ❗️Advanced (inversion — formal): Not for nothing + auxiliary + subject + verb • Not for nothing did he win that award. • Not for nothing is she considered the best. 🚫 Common mistakes ❌ I did it not for nothing (sounds awkward) ✅ I didn’t do it for nothing ✅I did it for a reason

One more 🔥

Ну мёд 🍯

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"The person you needed most will end up being the person who teaches you how to stand alone."

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Expecting people to give you what you give them is just setting yourself up for disappointment. The truth is simple: nobody owes you the same energy

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