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The line L has equation y = 5 - 2x. (a) Show that the point P (3, -1) lies on L. (b) Find an equation of the line perpendicular to L that passes through P.

(a) To confirm that point P lies on L, we must substitute x = 3 into the equation and see if we get y = -1. y = 5 - 2(3) = -1, therefore P lies on the line L (b) The gradient of the perpendicular line is -1/...
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Answered by Kitty S. • Maths tutor
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A gardener uses this formula to work out how much he charges to make a lawn. C = 7(14 +A)/ 3. C is the charge in £. A is the area in m2. He makes a rectangular lawn measuring 12.5 m by 17.6 m. How much does he charge?

Area of lawn = 12.5 x 17.6 = 220 m2 Substituting into the formula given the cost if found, C = 7(14 + 220)/3 = £546
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Answered by Kitty S. • Maths tutor
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How do I find f'(x) for f(x)=4x^3+x^2+5x+8?

This question require you to differentiate. The general rule for this format of differentiation is to multiply the number in front of the x by the power of the x and then reduce the power by one (in formula ...
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Answered by Naomi C. • Maths tutor
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Discuss hazard mitigation mechanisms developed for different threats posed by volcanoes (40 marks)

Across the globe, the theory of plate tectonics and evidence of shallow Earth structure processes has enabled scientists to determine the variety of hazards cause by different eruptive styles. Volcanoes pose...
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Answered by Daniel V. • Geography tutor
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Why is phenylamine a weaker base than ethylamine?

Phenylamine is a weaker base than ethylamine because the lone pair on the nitrogen atom in phenylamine is spread into the delocalised electron ring in benzene, therefore is less available for protonation tha...
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Answered by Adam J. • Chemistry tutor
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