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How does temperature relate to the structure of solids and liquids?

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 substan...
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Answered by Aditya R. • Physics tutor
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How should I approach a proof by induction question?

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 +...+ s...
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Answered by Aditya R. • Maths tutor
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What is the basic economic problem?

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.
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Answered by Drishti P. • Economics tutor
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find the coordinates of the turning points of the curve y = 2x^4-4x^3+3, and determine the nature of these points

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 setting t...
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Answered by Jenny N. • Maths tutor
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A circle has equation x^2+y^2-8x+10y+41=0. A point on the circle has coordinates (8,-3). Find the equation of the tangent to the circle passing through this point.

From the equation x 2 +y 2 -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,-5).Now we can find ...
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Answered by Joseph K. • Maths tutor
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