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y is inversely proportion to the square of x. y=10 when x=5. Express y in terms of x.

y is proportion to 1/x 2 . This can be written as y=k/x 2 where k is a constant of proportionality. Given that y=10 when x=5 , k can be found as yx 2 which is equal to 25. Therefore; y=25/x 2 .
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Answered by Evan H. • Maths tutor
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The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x 2 -2ax+8. At point B , x=4 . This gives the relation 104=8a and thus gives a=13.
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Answered by Evan H. • Maths tutor
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A heater uses energy from a laptop computer to keep a mug of coffee hot. Energy is transferred to the coffee at the bottom of the mug. Explain how a convection current is set up in the coffee.

The molecules at the bottom of the mug gain energy and spread out as a result. This means that these molecules are less dense than the ones above them so they rise upwards. As they do so, they lose energy to...
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Answered by Evan H. • Physics tutor
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The mercury atoms in a fluorescent tube are excited and then emit photons in the ultraviolet region of the electromagnetic spectrum. Explain (i) how the mercury atoms become excited and (ii) how the excited atoms emit photons.

(i) As they pass through the fluorescent tube, they collide with the mercury atoms within it and this collision transfers energy to the atom. This energy transfer allows the atom's orbiting electrons to move...
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Answered by Evan H. • Physics tutor
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Discuss the criminal liability of Mike

In this situation Mike would be charged with Murder. Murder is a common law offence. It was defined by Sir Edward Coke as the unlawful killing of a living human being, under the queen’s peace, with malice af...
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Answered by Gurjant B. • Law tutor
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