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Shifting vertically even-degree polynomial's graph by its mean over an interval
Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by...

4 days ago

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Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...

4 days ago

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Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...

4 days ago

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Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...

4 days ago

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[Mảng 1 Chiều Cơ Bản]. Bài 1. Chẵn lẻ
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là đếm xem trong mảng có bao nhiêu số chẵn, bao nhiêu số lẻ, tổng các phầ...

4 days ago

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[Mảng 1 Chiều Cơ Bản]. Bài 2. Trung bình cộng nguyên tố
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là tính trung bình cộng của các số là số nguyên tố trong dãy. Dữ liệu đảm...

4 days ago

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[Mảng 1 Chiều Cơ Bản]. Bài 3. Số nhỏ nhất
Cho mảng số nguyên A[] gồm N phần tử, hãy đếm xem trong mảng của bạn có bao nhiêu số có cùng giá trị nhỏ nhất. Ví dụ mảng A = {1...

4 days ago

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[Mảng 1 Chiều Cơ Bản]. Bài 4. Lớn hơn, nhỏ hơn
Cho mảng số nguyên A[] gồm N phần tử và số nguyên X , hãy đếm xem trong mảng có bao nhiêu số lớn hơn X và bao nhiêu số nhỏ hơn X...

5 days ago

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[Mảng 1 Chiều Cơ Bản]. Bài 5. In phần tử
Cho mảng số nguyên A[] gồm N phần tử, nhiệm vụ của bạn là in ra các phần tử là số chẵn ở chỉ số chẵn, nếu mảng không tồn tại phầ...

5 days ago

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Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...

5 days ago

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Gather primes
A book titled Gather that I regularly see inspired this game: make as many words as possible from the letters in the word GATHER...

5 days ago

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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...

5 days ago

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Built-out FFTShift
The task in hand is to replicate the built-in function - fftshift (with single input), but without using the function. However,...

5 days ago

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The Square Tree of Power
As Arjun crosses the Dividing River, he enters a sacred clearing where a giant glowing tree stands in the center. This is the le...

5 days ago

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The Triangle Stone of Destiny
After passing the Square Tree, Arjun reaches the entrance of a hidden cave. In front of the cave lies a glowing triangular stone...

5 days ago

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The Square Tree of Power
As Arjun crosses the Dividing River, he enters a sacred clearing where a giant glowing tree stands in the center. This is the le...

5 days ago

Solved


The Equation Guardian
After activating the Circle of Protection, Arjun walks deeper into the cave and reaches a massive stone door. Suddenly, a giant ...

5 days ago

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Velocity at Bottom Using Energy Conservation
A steel ball rolls down a precision ramp in a lab at CERN.

5 days ago

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Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...

5 days ago

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Angular Velocity Required to Create Artificial Gravity
Scientists at NASA and Indian Space Research Organisation are designing a rotating space station ring to simulate Earth-like gra...

5 days ago

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Moment of Inertia Using Parallel Axis Theorem
Engineers at Indian Space Research Organisation are designing a satellite with extendable robotic arms. When the arms extend out...

5 days ago

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Velocity of a Particle Under Constant Acceleration Using Energy Methods
Scientists at CERN are testing a linear accelerator that uses electromagnetic force to accelerate charged particles along a stra...

5 days ago

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Acceleration in a Symmetric Double-Pulley Constraint System
Engineers at Indian Institute of Technology Kanpur are designing a precision counterweight system for high-speed elevators. The ...

5 days ago

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Tension in String for Circular Motion (Advanced Rotational Dynamics)
At the astronaut training facility of Indian Space Research Organisation, astronauts are trained using a rotating centrifuge. Th...

5 days ago

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Angular Velocity of a Falling Rod Pivoted at One End (Energy + Rotation)
Engineers at Indian Institute of Technology Bombay are designing a rotating docking arm for a future space station. The arm is m...

5 days ago

Solved


Motion of a Bead Sliding on a Rotating Rod (Non-Inertial Frame Dynamics)
Scientists at Indian Space Research Organisation are testing artificial gravity inside a rotating space station module. Inside ...

5 days ago

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Acceleration of Block Relative to Ground
Researchers at Indian Space Research Organisation test cargo motion inside accelerating spacecraft ramps. Find acceleration.

5 days ago

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Acceleration in an Atwood Machine with Massive Pulley
Engineers at Indian Institute of Technology Delhi are designing a precision elevator calibration system using two masses connect...

5 days ago

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Power of Moving Vehicle
Engineers at Tesla calculate how much power is required to maintain vehicle motion.

5 days ago

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Spring Energy Storage
Engineers at Bosch design suspension systems using springs. They calculate the energy stored when the spring compresses.

5 days ago

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