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¿Qué te gusta hacer en tu tiempo libre?

This question is to help with the speaking exam for GCSE. It is a very common question asked by examiners as it allows the student to show off vocabulary that they have learnt and allows different tenses ...

Answered by • Spanish tutor

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A circle has equation: (x - 2)^2 + (y - 2)^2 = 16. It intersects the y-axis (y > 0) at point P and the x-axis (x < 0) at point Q. Find the equation of the line connecting P and Q and of the line perpendicular to PQ passing through the circle's centre.

(x - 2)² + (y - 2)² = 16 x = 0 --> 4 + (y - 2)² = 16 --> y - 2 = ±2sqrt{2} --> y = 2 ± 2sqrt{2} --> P(0,2 + 2sqrt{2})y = 0 --> (x - 2)² + 4 = 16 ...

Answered by • Maths tutor

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Show that (x + 1)(x + 2)(x + 3) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are positive integers.

(x + 1)(x + 2) = x^2 + 2x + x + 2 = x^2 + 3x+2therefore(x + 1)(x + 2)(x+3)= (x^2+3x+2)(x+3) = x^3 + 3x^2 + 2x + 3x^2 + 9x + 6 = x^3 + 6x^2+ 11x + 6where a=1 b=6 c=11 and d=9expansion of brackets can be do...

Answered by Jeremy T. • Maths tutor

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Using the factor theorem, factorise x^4 - 3x^3 - 3x^2 + 11x - 6

Well the question states that it wants you to use the factor theorem so it would be a good idea to write down the factor theorem to remind ourselves."A polynomial f(x) has a factor (x - a) if and onl...

Answered by Kester G. • Maths tutor

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(a) Explain what is meant by monopoly and, using a diagram, explain why a monopoly may have lower average costs of production than a firm in perfect competition. [10]

· Definition and examples of different types of monopoly.I.e. pure, natural, and local monopolies.High barriers to entry&exit / price-makers.· Definition of perfect competition.Many buye...

Answered by Ethan S. • Economics tutor

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