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A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.

Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is, w...
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Answered by Oliver L. • Maths tutor
9618 Views

Rewrite ... logF=logG+logH−log(1/M)−2*logR ... in the form F=... using laws of logarithms

logF=logG+logH−log(1/M)−2*logR Simplify RHS using law of logarithms, logF=log(G H)−log(1/M)−2logR using law of addition logF=log(G H M)−2 logR using law of subtraction logF=log((G H M)/R^2)) using law of pow...
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Answered by Ambrose R. • Maths tutor
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Find the stationary point on the line of y = 6x - x^2 and state whether this point is a maximum or a minimum

This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation --> if y = x n then dy/dx = nx n-1 Therefore if y = 6x - x 2 ,...
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Answered by Percy W. • Maths tutor
6510 Views

A circle is given by the equation x^2+y^2-20x-24y+195=0. Draw this circle.

In order to answer this question, we must transform this equation for a circle into the general form of an equation of a circle; namely something like (x-a) 2 +(y-b) 2 =r 2 . Once we have done this, we know ...
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Answered by Bea A. • Maths tutor
7186 Views

Solving a quadratic with ax^2 e.g. 2x^2 - 11x + 12 = 0

To solve the equation in the form (ax + b)(x + c): Method 1 Rewrite the x term as the sum of 2 different x terms. Start by multiplying the x^2 term and the final number term, to give 24. The two x terms shou...
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Answered by Andrea W. • Maths tutor
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