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Differentiate y=x^2 from first principles

y=x²dy/dx= Lim_h-->0( ((x+h)²-x²) / (x+h-x) )dy/dx= Lim_h-->0( (x² + 2hx + h² - x²) / h )dy/dx= Lim_h-->0...

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A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sin⁡θ=1/√6 and the line intersects the plane at z = 0. Find p and q.

This question gives hints as to how you should solve it. Because it tells you the angle between the line and the plane, this should indicate that doing something to do with finding the angle between the l...

Answered by Joss O. • Further Mathematics tutor

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(Henry VIII module) Describe the opposition that Henry VIII encountered in the years 1532-1535 to his proposed changes to the position and role of the Church and Pope in England. (20 marks)

Henry VIII intended to implement the 'Royal Supremacy' between 1532 - 1535, whereby the Pope's jurisdiction over matters in England would cease. The British Monarch would also become the Head of the Churc...

Answered by Usman A. • History tutor

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Solve 4log₂(2)+log₂(x)=3

First, we should look at the laws of logarithms.log_ax+log_ay=log_axylog_ax-log_ay=log_a(x/y)klog_ax=log_ax^kWe ca...

Answered by • Maths tutor

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How do I understand the French in listening exams when they speak so much more quickly than GCSE?

As fast as they sound, there is a simple solution when it comes to Listening exams. The more you listen to spoken French, the more familiar you get with it and the more at ease you are with the speed. It ...

Answered by Alexandra W. • French tutor

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