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Why does differentiation work like it does.

Differentiation is about the tangent at a point, from GCSE we have a formula to work out the gradient between two points, in other words, the gradient of the tangent. This means that as the two points get in...
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Answered by Lucas F. • Maths tutor
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(a) Express (1+4*sqrt(7))/(5+2*sqrt(7)) in the form a+b*sqrt(7), where a and b are integers. (b) Then solve the equation x*(9*sqrt(5)-2*sqrt(45))=sqrt(80).

(a) We can ‘get rid of’ a square root in the denominator simply by multiplying by 1 (value of the fraction stays unchanged) in a suitable form. We will take advantage of this formula: (a+b) (a-b)=a^2-b^2. So...
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Answered by Kristina B. • Maths tutor
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Find the equation of the tangent to the curve y=3x^2-7x+5 at the point (2, 3) .

The starting point for a question like this is to differentiate the function - in this case the curve y=3x 2 -7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested in the case wh...
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Answered by Matthew S. • Maths tutor
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Approximately how long is a double-stranded DNA molecule with a molecular weight of 3x10^9 g/mol? Assume the molecular weight of one nucleotide is 333 g/mol, and that there are 10 base pairs for each turn of the DNA helix equalling 3.4nm in length.

Let's begin by assessing the molecule. If we divide the molecular weight by two, that will give us the weight for one strand of the helix. Knowing that one nucleotide is 333 g/mol, then dividing the weight o...
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If a solution, contained in a 1cm cuvette, has an absorbance value of of 0.865 A.U, and concentration value of 2mM. What is the value regarding the molar extinction coeffient?

Firstly, using Beer-Lambert's equation. It is noted, that absorption is equal to the molar extinction coefficient, multiplied by the path length of light, multiplied by the concentration of the solution.Ther...
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Answered by Aaron V. • Chemistry tutor
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