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Work out the equation of the tangent at x = 3, knowing that f(x) =x^2

Currently, we know that:f(x) = x 2 To find the equation of the tangent you need the gradient and the y-value of the graph at x = 3So, you can differentiate f(x):f'(x) = 2xlet x = 3: f(x) = 9 f'(x) = 6the equ...
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Answered by Arnav A. • Maths tutor
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What is the order of decreasing acidity for the molecules phenol, ethanoic acid and ethanol? Why?

Ethanoic acid is the most acidic of the three. This is because once ethanoic acid has lost a proton the negative charge can be spread over two oxygen atoms via two resonance forms. Oxygen atoms are electrone...
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Answered by Dan T. • Chemistry tutor
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A railway car of mass m1 travelling at a velocity of v1 collides with a second car of mass m2 travelling at v2 and the two join together. What is their final velocity?

Momentum is conserved in any collision, and for a single body is given by p = mv. The momentum before is m1 v1+m2 v2, and the momentum after is (m1 + m2) u where u is the final velocity, so the final velocit...
Answered by • Physics tutor
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For which values of k does the quadratic equation 2x^2+kx+3=0 only have one unique solution?

A quadratic equation ax 2 +bx+c=0 will have only one unique solution if and only if b 2 -4ac=0. If we apply this to the equation in the question, we get that k 2 -24=0. If we solve this equation we get two s...
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Answered by Ewan R. • Maths tutor
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How should i answer an unseen poetry question in an exam? (AQA)

Firstly, it is important to remember the five areas you will be marked on. These are: AO1: articulate informed, personal and creative responses to literary texts, using associated concepts and terminology, a...
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Answered by Corrine C. • English tutor
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