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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...
LF
Answered by Lucas F. • Maths tutor
3645 Views

(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...
KB
Answered by Kristina B. • Maths tutor
8750 Views

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...
MS
Answered by Matthew S. • Maths tutor
8130 Views

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...
AV
11247 Views

Explain how during a game of a rugby, an increase in blood Co2 will cause heart rate to rise (4 marks)

As the muscles in the body respire and use up the oxygen, Co2 is produced and thus blood acidity in the bloodstream rises 2) This change is detected by the chemoreceptors 3) These impulses are then sent to t...
TM
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