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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...
JD
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...
JS
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...
JS
Answered by Joshua S. • Philosophy tutor
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What is the Tripartite Theory of knowledge?

The Tripartite Theory of knowledge states that if a belief is true and that we are justified in holding this belief then it is knowledge. The belief here comes in the form of a propositional concept held as ...
CS
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A projectile is launched from the ground at a speed of 40ms^-1 at an angle of 30 degrees to the horizontal, where does it land? What is the highest point the projectile reaches?

Since the SUVAT equations of motion act independently in the horizontal and vertical directions we can use the vertical equations to find the total time (the time when total vertical displacement is zero) an...
BL
Answered by Ben L. • Physics tutor
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