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f(x) = 2x3 – 5x2 + ax + 18 where a is a constant. Given that (x – 3) is a factor of f(x), (a) show that a = – 9 (2) (b) factorise f(x) completely. (4) Given that g(y) = 2(33y ) – 5(32y ) – 9(3y ) + 18 (c) find the values of y that satisfy g(y) = 0, givi

a) 54-45+3a+18=0 3a+27=0 3a=-27 and thus a=-9b) 2x^3 – 5x^2 -9x + 18 = (x-3) (2x^2 +bx-6)to find b ; collect the x^2 terms so bx^2-6x^2=-5x^2 and thus b=1c) when comparing f(y) and f(x) we see that x=3^2yf(x...
AK
Answered by Akrit K. • Maths tutor
8997 Views

Differentiate e^x^2

e x^2 --------> dy/dx = 2xe x^2
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Answered by Connor C. • Maths tutor
4957 Views

Use integration by parts to find the value of definite integral between 5 and 1 (3x/root(2x-1))dx

use the formula integral(u v') = u v - integral(v u') so the tricky integral can be avoided (this formula can be derived from integrating the product rule) so in these questions all you need to look for is w...
MG
Answered by Matthew G. • Maths tutor
6294 Views

Find the differential of the equation: x^2(2x+5)

First expand the equation, giving us 2x^3 + 5x^2Then you can differentiate the equation by multiplying the number at the front of x by its power.Only then, we need to subtract 1 from the power.This gives us ...
JM
Answered by Jayant M. • Maths tutor
3843 Views

A uniform ladder is leaning against a smooth wall on a rough ground. The ladder has a mass of 10 kilograms and is 4 metres long. If the ladder is in equilibrium, state an equation for the coefficient of friction of the ground

Uniform means that the centre of mass is half way up the ladder. Smooth wall means no friction is felt on the wall and rough ground means that there is friction felt there. First, draw a diagram and take mom...
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Answered by Alexandra A. • Maths tutor
6341 Views