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Explain the trend of first ionisation energy down a group.

The first ionisation energy is the energy required to remove one electron from an atom. Down a group, there are more electron shells surrounding the nucleus, which results in a greater shielding from the nuc...
RW
Answered by Rachael W. • Chemistry tutor
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g(x) = ( x / (x+3) ) + ( 3(2x+1) / (x^2 + x - 6) ). Show that this can be simplified to: g(x) = (x+1) / (x-2).

Step 1: The denominator of the right-hand fraction is quadratic, so we can factorise this to (x+3)(x-2). This looks similar to the denominator of the left-hand fraction, suggesting we can combine the two. St...
AS
Answered by Amar S. • Maths tutor
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Give TWO similarities in the movement of substances by diffusion and by osmosis.

(Movement) down a gradient / from high concentration to low concentration; 2. Passive / not active processes; OR Do not use energy from respiration / from ATP / from metabolism; OR Use energy from the soluti...
MS
Answered by Murtaza S. • Biology tutor
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A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differenti...
CM
Answered by Carlotta M. • Maths tutor
4599 Views

Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0

(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually) if (1+x)^3 &gt; 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 &gt; 1 + 3x^2 + x^3 3x &gt; ...
VT
Answered by Vigneswaran T. • Maths tutor
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