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How to find the reciprocal of a graph, such as y=cos(x)?

To find the reciprocal of any graph, first consider the key points, in this case: (0,1), (90,0), (180,-1), (270,0) and (360,1). Since we are finding the reciprocal in the y-axis, we can find the reciprocal o...
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Answered by Aqeel A. • Maths tutor
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Explain the difference between Libetarianism and Hard Determinism. Discuss which is the stronger argument.

Libertarianism is the claim that human individuals have autonomous control over their actions, and are, therefore, morally accountable agents. Hard determinism, on the other hand, claims that an individual's...
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Distinguish between a codified and an uncodified constitution.

A codified constitution is a single, written document that underpins the nature and structure of governance within a state. Codifed constitutions will usually outline the powers of different branches of gove...
JH
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A trillion is 10^12. Which of the following is bigger: the three trillionth root of 3 or the two trillionth root of 2? You may assume that if 0 < x < y, then 0 < x^n < y^n for integer values of n greater than or equal to 1.

For this sort of question, the easiest approach is to make an educated guess at the correct answer, and prove that this must be correct by contradiction. As taking the root of something has a large effect on...
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Answered by Benjamin C. • MAT tutor
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Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.

In order to find the equation of the tangent to a curve at a point (x 1 , y 1 ), we use the equation y - y 1 = m(x - x 1 ), where m is the gradient of the curve at (x 1 , y 1 ). We already have x 1 = √3, so ...
BC
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