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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...

KB
Answered by Kristina B. Maths tutor
7466 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=3x2 -7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested i...

MS
Answered by Matthew S. Maths tutor
7140 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 wei...

AV
9423 Views

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.T...

AV
Answered by Aaron V. Chemistry tutor
1472 Views

Why does tanx = sinx/cosx ?

This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse side...

SR
11775 Views

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