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show that y = (kx^2-1)/(kx^2+1) has exactly one stationary point when k is non-zero.

Stationary points are found by considering the points at which the gradient of the function equal zero. For the above, you need to employ the quotient rule, since both numerator and denominator are f(x), ...

Answered by Rob M. • Maths tutor

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A ball is projected vertically upwards from the ground with speed 21 ms^–1. The ball moves freely under gravity once projected. What is the greatest height reached by the ball?

Set out information given in question, and taking the upward direction to be positive: s (displacement) = ?, u (initial speed) = 21ms^-1, v (final speed at maximum height) = 0ms^-1, a ...

Answered by Shruti S. • Maths tutor

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Solve 7x + 6 > 1 + 2x

7x + 6 > 1 + 2xFirst, we collect the like terms so we move all the x's to one side and all the integers to the other:5x > -5Then we divide by 5 on each side to find what just x will be.Therefore, x ...

Answered by Juliet Z. • Maths tutor

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Let C : x^2-4x+2k be a parabola, with vertex m. By taking derivatives or otherwise discuss, as k varies, the coordinates of m and, accordingly, the number of solutions of the equation x^2-4x+2k=0. Illustrate your work with graphs

Write y=x²-4x+2k. And m:= (x_m, y_m) for the coordinates of our vertex. We deduce that x_m is exactly the value of x for which y'=2x-4=0, because m is a minimum p...

Answered by Massimiliano V. • Maths tutor

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Solve the simultaneous equation, 3x + y = 8 and x + 3y = 12, to find a value for x and y.

Re arrange one of the equation to get a single variant answer. So, x = 12 - 3y. Substitute this into the other equation, so 3 (12-3y) + y = 8. Expand this equation to form 36 - 9y + y = 8. Collect the y t...

Answered by Grace R. • Maths tutor

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