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i) Using implicit differentiation find dy/dx for x^2 + y^2 = 4 ii) At what points is the tangent to the curve parallel to the y axis iii) Given the line y=x+c only intersects the circle once find c given that c is positive.

I don't know how effectively I can communicate this answer via text without the whiteboard but I'll try. i) First implicitly differentiate with respect to x: 2x + 2y * dy/dx = 0. Rearranging gives dy/dx = -x...
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Answered by James D. • Maths tutor
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Solve the simultaneous equations, 2x+y-5=0 and x^2-y^2=3

2x+y-5=0, y=5-2x (put into second equation) x 2 -y 2 =3, substituting in we get, x 2 -(5-2x) 2 =3, expand, x 2 -(25+4x 2 -20x)=3, simplify, x 2 -25-4x 2 +20x=3, 0=3x 2 -20x+28, put into brackets by seperatin...
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Answered by Joshua S. • Maths tutor
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Explain why, for Locke, extension is a primary quality?

Locke founded the idea that we perceive qualities differently. He argued that primary qualities such as extension, size, shape and weight do not change when we perceive them. They are mind independent, objec...
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Answered by Joshua S. • Philosophy tutor
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How do you know which case to use after German prepositions?

There are three possible cases that follow prepositions: accusative, dative or genitive. The following prepositions are followed by the accusative case: bis,durch, fuer, gegen, ohne, um Example- Ich will ohn...
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Answered by Thorkild V. • German tutor
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How do I structure an essay?

The most important part of an essay is making sure the points you are making are clear, and the best way to do this is with the structure. Firstly, make sure there is a clear introduction which lays out your...
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Answered by Emily W. • History tutor
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