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By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)

Answer : y = 3/x 2 + c/x 4 Integrating factor is 4/x (1 mark) => I = e integral (4/x) dx (1 mark) => I = x 4 (1 mark) . Using the formula, d/dx (x 4 y) = 6x (1 mark) => x 4 y = integral(6x)dx (1 mar...
MD
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A curve has the equation y=sin(x)cos(x), find the gradient of this curve when x = pi. (4 marks)

Option 1 - Differentiate using product rule giving dy/dx = cos 2 (x) - sin 2 (x). (2 marks) Subbing in x as pi (1 mark) then gives (-1) 2 + (0) 2 . Therefore the gradient is 1 (1 mark) . Option 2 - Initially...
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Answered by Mark D. • Maths tutor
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Iqbal Khan’s production of Othello (2015) breaks with tradition in casting both Othello and Iago as black men - in what way does this shift the emphasis of the play?

Often dubbed a 'race play', Shakespeare's 'Othello' usually pits the jealousy of a white man against the success of a Moor, illustrating the destructive consequences of racial intollerance. Khan's casting de...
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Answered by Michael M. • English tutor
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Explain the general trend in first ionisation energy across period 2 in the periodic table.

Across period 2, the nuclear charge increases from Li (3+) to Ne (10+) as protons are added to the nucleus. - The electros are removed from the same main energy level and electrons in the same main energy le...
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Answered by Eyad A. • Chemistry tutor
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If a ball is thrown on the Moon, the projectile would have a greater range than if it were to have been thrown on Earth. Why is this the case?

The Moon has a lower gravitaional field strength than the Earth, and it does not have an atmosphere. The lower gravitational field strength means that there is lower acceleration, which results in an increas...
TD
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