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Differentiate y = e^(x^2 - 3x).

This question is an example of the chain rule for differentiating. Firstly, identify the inner function. In this case, it is x 2 - 3x. This function must be differentiated first: d/dx (x 2 - 3x) = 2x - 3 Sec...
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Answered by Ellie S. • Maths tutor
13493 Views

Find cos4x in terms of cosx.

As with any question involving sines and cosines, consider complex numbers as a likely way to find the answer. For this particular kind of question, where sin/cos of a multiple of x is needed in terms of sin...
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Answered by Ellie S. • Maths tutor
21134 Views

How does antibiotic resistance develop in bacterial populations?

When a course of antibiotics is taken, non-resistant bacteria should be killed. However, genetic mutations can lead to certain individuals becoming resistant to a particular antibiotic. The mutated gene that...
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Answered by Callum D. • Biology tutor
6952 Views

A cricketer throws a ball vertically upwards so that the ball leaves his hands at a speed of 25 m/s. Calculate the maximum height reached by the ball, the time taken to reach max. height, and the speed of the ball when it is at 50% max. height.

We can see that this is a suvat question, since it involves a projectile. The first step for any suvat question is to list the known suvat variables for the point we're looking at (in this case, the point of...
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Answered by Ellie S. • Physics tutor
22476 Views

How do I use "y" and "en" in sentences?

The concept of "y" and "en" can be difficult to grasp at first, as both words are often used quite idiomatically, and can be translated in a number of different ways. Y and en are adverbi...
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Answered by Callum D. • French tutor
31883 Views