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i) Simplify (2 * sqrt(7))^2 ii) Find the value of ((2 * sqrt(7))^2 + 8)/(3 + sqrt(7)) in the form m + n * sqrt(7) where n and m are integers.

i) (2 sqrt(7)) 2 = 2 2 sqrt(7) 2 = 4 * 7 = 28 (1 mark) ii) First of all substitute the answer from above. ((2 * sqrt(7)) 2 + 8) / (3 + sqrt(7)) = (28 + 8) / (3 + sqrt(7)) = 36 / (3 + sqrt(7)) Multiply by (3 ...
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Answered by Andrew B. • Maths tutor
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Find the equation of the tangent to the curve y = (5x+4)/(3x-8) at the point (2, -7).

Firstly, we need to find the gradient at this point on the curve as the tangent will have the same gradient. So to find the gradient of the curve or in other words, dy/dx, we differentiate the equation. To d...
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Answered by Manika S. • Maths tutor
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A ball is fired from a cannon at 20m/s at an angle of 56degrees to the horizontal. Calculate the horizontal distance the ball travels as well as its maximum height reached.

This is a typical mechanics question in an AS/A-level exam and uses the principles of SUVAT and projection. We can try to calculate the maximum height reached first using the veritical components. SUVAT: s=?...
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Answered by Aaron F. • Maths tutor
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How would I differentiate a function such as f(x)=x^3(e^(2x))?

Here, f(x)=x 3 e 2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(x)+u'(x)v(x). The firs...
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Answered by Lauren B. • Maths tutor
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Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the frac...
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Answered by Omar G. • Maths tutor
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