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How do I find the stationary points on the curve y = f(x) = x^3+6x^2-36x?

When trying to find stationary points, the first thing you should think about is differentiating. At a stationary point, the gradient of a curve or function is equal to zero. Therefore if we differentiate th...
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Answered by Luke S. • Maths tutor
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Given y=x^2(1+4x)^0.5, show that dy/dx=2x(5x+1)/((1+4x)^0.5)

You have to differentiate the equation y=x^2(1+4x)^0.5 with respect to x to get dy/dx and thereby prove the result in the question. An equation composed of the product of two x terms can be differentiated wi...
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Answered by Alistair G. • Maths tutor
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A Uranium-(238,92) nucleus decays into a Thorium-234 nucleus by the emission of an alpha-particle. Given Thorium has a chemical symbol Th build a nuclear equation.

A nuclear equation expresses all of the elements before (LHS of = sign) and after (RHS of = sign) the reaction in terms of nucleon (N) and proton number (A), both quantities are conserved during the reaction...
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Answered by Alistair G. • Physics tutor
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Describe how a PET scan works?

A PET scan which is known as Positron Emission Topography involves passing a positron emitting source through a patient. The source used for a PET scan is FDG which contains Fluorine-18. A positron emitted b...
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Answered by Arjun S. • Physics tutor
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Describe and explain the photoelectric effect in terms of photons interacting with the surface of a metal.

The photoelectric effect occurs when individual photons are incident on a clean metal surface. The photons are absorbed by electrons in the clean metal surface and they are released as photoelectrons. The in...
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Answered by Arjun S. • Physics tutor
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