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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 ha...

NA
Answered by Nazar A. Maths tutor
15935 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, whi...

EO
Answered by Eloise O. Biology tutor
16327 Views

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 ...

HM
Answered by Harry M. Biology tutor
3745 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 = (H2+R2)1/2 V = (1/3)πR2(H2+R2)1/2

dV/dt = -k

dH/dt = dH/dV × dv/dt

dV/dH = (1/3)πR2H(H...

CE
Answered by Callum E. Maths tutor
3800 Views

Integrate the following function: f(x) = ln(x)

∫ln(x)dx = xln(x) - ∫x/x dx = xln(x) - x + C

CE
Answered by Callum E. Maths tutor
3638 Views

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