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f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we have ...
NA
Answered by Nazar A. • Maths tutor
16277 Views

Describe and explain the effects of pH, temperature, enzyme concentration and substrate concentration on enzyme activity

pH : All enzymes have an optimum pH value which is very specific. This is because hydrogen ions and hydroxide ions have very significant changes on the tertiary structure of an enzyme, which can cause substr...
EO
Answered by Eloise O. • Biology tutor
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How do I structure an essay about a character?

First, it would be helpful to make a brief plan (10 minutes), that outlines your points (4 or 5 points). Things to think about are narrative style, dialogue, themes, motifs, character traits, etc. Then pick ...
AJ
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Putting bee honey on a cut kills bacteria. Honey contains a high concentration of sugar. Use your knowledge of water potential to suggest how putting honey on a cut kills bacteria.

Once honey is added to an infected cut, the osmotic gradient favours water moving from the bacterial cells to the honey. This is because the water potential is lower in the honey. As a result of the loss of ...
HM
Answered by Harry M. • Biology tutor
3917 Views

Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H 2 +R 2 ) 1/2 V = (1/3)πR 2 (H 2 +R 2 ) 1/2 dV/dt = -k dH/dt = dH/dV × dv/dt dV/dH = (1/3)πR 2 H(H 2 +R 2 ) 1/2 Thus, dH/dt = -3k/(πR 2 H(H 2 +R 2 ) 1/2 ) ​​​​​ ​​​​ ​​
CE
Answered by Callum E. • Maths tutor
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