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Using Algebra show that part of the line 3x + 4y = 0 is a diameter of the circle with equation (x^2) + (y^2) = 25

To show that the line is a diameter of the circle you muct show that it goes through the centre of the circle1) finding the centre of the circle. The general eqn is (x-a) 2 + (y-b) 2 = r 2 , where r is the r...
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Answered by Emma L. • Maths tutor
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How do I find a stationary point on a curve and work out if it is a maximum or minimum point?

At any stationary point, the gradient of a line is zero. Therefore dy/dx = 0. If we differentiate the equation of the line, and solve this expression we can find the coordinates of the stationary point. If w...
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Answered by Benjamin H. • Maths tutor
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How do you integrate the natural logarithm ln(x)?

To integrate this function, we must first recognise that ln(x) can be treated as 1 multiplied by ln(x). Using this knowledge, we can apply the 'integration by parts method' to integrate the function.Formula:...
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Answered by Andrew A. • Maths tutor
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Finding complex numbers using DeMoivre's Theorem

Find the cube roots of 2 1/2 cis(pi/4) 2 1/2 cis(pi/4+ 2pi k), for every integer k By DeMoivre: 2 1/2 1/3 cis((pi/4+ 2pi k)/3) 3 2 1/6 cis(pi/12+ 2/3 pi *k) Taking k=0,1,2 gives the three cube roots:z 1 = 2 ...
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Answered by Lisa R. • Maths tutor
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Differentiate y=(x-1)^4 with respect to x.

Using the chain rule, differentiate the "outside function" and the "inside function", and multiply the two results to get:dy/dx = 4(x-1)^3 * 1 = 4(x-1)^3
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Answered by Samuel H. • Maths tutor
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