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Temperature is defined as the average kinetic energy of a substance, and it is what determines whether an object is a solid or a liquid. When the temperature is low, the average kinetic energy of the subs...

Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +......

The economic problem – sometimes called basic or central economic problem – asserts that an economy's finite resources are insufficient to satisfy all human wants and needs.

To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and settin...

From the equation x²+y²-8x+10y+41=0, we can find the centre of the circle by the middle two terms -8x+10y and multiplying them by -1/2. So the coordinates of the circle centre are (4...