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Given that y= x/(2x+5), find dy/dx

Is it integration or differentiation? Differentiation What rule do we use? Since it's a fraction, use the quotient rule Is the rule in the formula book? Yes Identify what u and v equal too. u = x and v = 2x ...
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Answered by Salma A. • Maths tutor
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Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x^(2) + y^(2) = 5

If a line is a tangent to a circle, it will have exactly one point where the line intersects the circle. Therefore, when we set the equation of the straight line equal to the equation of the circle, we shoul...
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Answered by Rawdah H. • Maths tutor
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On the same diagram, sketch the graphs of: y = |5x -2| and y = |2x| and hence solve the equation |5x - 2| = |2x|

y = |2x| is a "V" shaped graph with a gradients of 2 and -2 that inflects at the origin (0,0)y = |5x - 2| is a "V" shaped graph with gradients of 5 and -5 that inflects at the point (2/5,...
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Answered by Charlie P. • Maths tutor
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Differentiate x^2 from first principles

Differentiation is about finding gradients of functions. With straight lines we take the "rise of run" - the change in y over the change in x. With curves e.g. f(x) = x^2 we need to use the same id...
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y is inversely proportional to d^2 and when d = 10, y = 4. d is directly proportional to x^2 and when x = 2, d = 24. Find a formula for y in terms of x. Give your answer in its simplest form.

Firstly, find proportionality equation between the two variables. This should be shown as d = kx^2 and y = b/d^2.Solve to find constants of proportionality of a=6 and b=400. Eliminating for d, find that y=10...
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