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theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec 2 (θ)dθ/dx = 5 Use identity sin 2 (θ) + cos 2 (θ) = 1, dividing through by cos 2 (θ), to get 2(1+tan 2 (θ))dθ/d...
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Answered by Callum W. • Maths tutor
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How do I remember what grammatical gender nouns have?

It is essential to know what grammatical gender german nouns possess as these will determine the endings of articles and adjectives of the sentences we create. As a result I would always suggest that every t...
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Answered by Stefania S. • German tutor
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Explain why chlorine has a lower boiling point than Bromine. (2 marks)

Chlorine molecules are smaller than bromine molecules in size, therefore, the van der Waals forces (intermolecular forces) are weaker between Cl2 molecules than compared to Br2 molecules.
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Answered by Joseph B. • Chemistry tutor
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Bob sprints down a 100 metre track as fast as he can and as he arrives at the finish, a light gate cuts a timer that has been active since Bob began his sprint. It reads 12.45 seconds. calculate Bobs average speed during the sprint.

s=distance/time = 100/12.45 =8.03m/s
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Answered by Richard W. • Maths tutor
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A cylindrical rod of radius 7mm and Young’s Modulus 70 GPa has a weight F applied to it. The material experiences a strain of 0.2%. What force has been applied?

Young's Modulus is defined as the ratio of stress to strain. E = stress/strain. Stress is the force per unit area, F/A. By substitution, we can see that E = F/(A x strain). Rearranging gives F = E x A x stra...
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Answered by Callum W. • Physics tutor
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