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ABCDEF is a regular hexagon (I will sketch this in the session). Find the angle DAF

What do we know about hexagons? They have six angles and vertices. The fact that the hexagon is regular implies that all interior angles are the same. We can split the hexagon up into six triangles. These...

JM
Answered by Jordan M. Maths tutor
13391 Views

How do you show that (x+2) is a factor of f(x) = x^3 - 19x - 30, and then factorise f(x) completely?

A1) Showing that (x+2) is a factor of f(x).         General Method:  If A is a number, then (x- A) is a factor of f(x) if when x=A,  f(x=A)=0    <-- This is what we want to show                        ...

RW
Answered by Rebecca W. Maths tutor
8685 Views

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
13698 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
3251 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
2934 Views

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