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Find the stationary points of the curve f(x) =x^3 - 6x^2 + 9x + 1

Step One: stationary/turning points are points on the curve where the gradient equals 0 (i.e. a point at which the slope changes from negative to positive, or vice versa). So we need to find the gradient of ...
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Answered by Angharad L. • Maths tutor
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Describe three effects of smoking on the alveoli

Answers could include:Thinning of alveoli walls to reduce the size of the alveoli air sacsSacs lose their elasticity leading to a difficulty in expelling carbon dioxide and taking in oxygenDecrease in diffus...
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Answered by Tash B. • Biology tutor
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How do I write a strong introduction, and what should it contain?

A strong introduction provides your examiner with a strong first impression. It introduces your writing style, and should establish the direction that your essay will take. Begin by highlighting key words wi...
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Solve the following equations. Leave answers in simplest terms a)e^(3x-9)=8. b) ln(2y+5)=2+ln(4-y)

a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Another ...
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Answered by Ben W. • Maths tutor
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a) show that (cosx)^2=8(sinx)^2-6sinx can be written as (3sinx-1)^2=2 b)Solve (cosx)^2=8(sinx)^2-6sinx

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement, w...
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Answered by Ben W. • Maths tutor
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