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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...

Answered by Nazar A. • Maths tutor

15827 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^...

Answered by Callum E. • Maths tutor

3765 Views

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

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

Answered by Callum E. • Maths tutor

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Solve the simultaneous equations 3x+5y=7, 2x-3y=11

Multiply the first equation by 2, and the second by 3:

6x+10y=14

6x-9y=33

Subtract the second from the first:

19y=-19

solve for y:

y=-1

plug in to first eq...

Answered by Jamie B. • Maths tutor

9383 Views

Why is the differential of a constant zero?

Any constant (say k) can be rewritten as kx⁰ since x⁰=1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest...

Answered by Jawad C. • Maths tutor

3921 Views