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g(x) = e^(x-1) + x - 6 Show that the equation g(x) = 0 can be written as x = ln(6 - x) + 1, where x<6

0 = e^x-1+ x - 6 e^x-1= 6-x x-1 = ln (6-x) -> here we have taken the natural log of both sides, but it only shows on one side as the natural log of e is 1.x = ln (6-x) + 1Question ...

Answered by Sumrah N. • Maths tutor

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Find the coefficient of x^4 in the expansion of: x(2x^2 - 3x + 1)(3x^2 + x - 4)

Only the terms which will form the x⁴ term need to be considered:x * 2x² * x + x * -3x * 3x² = -7x⁴Therefore the answer is -7.

Answered by Finn H. • Maths tutor

4199 Views

An object of mass 3kg is held at rest on a rough plane. The plane is inclined at 30º to the horizontal and has a coefficient of friction of 0.2. The object is released, what acceleration does the object move with?

We need to use Newtons law F=ma going down the slope.
We can see that the only forces acting in this direction are the component of the weight and friction, so we have that: F = Wsin30 - μR = 3a

Answered by Asha D. • Maths tutor

2828 Views

Show that (sec(x))^2 /(sec(x)+1)(sec(x)-1) can be written as (cosec(x))^2.

( sec²(x))/((sec(x)+1)(sec(x)-1))Then, by the rule of 'difference of two squares', we know that this equals= (sec²(x))/(sec²(x)-1)= (sec²x/tan²x)s...

Answered by Rishi S. • Maths tutor

10042 Views

Find the values of A between and including 0 and 360 degrees for tan(2A) = 3tan(A)

You cannot work with this equation in the current form so you must use identities to find an equivalent form that you can work with. It is known that tan(2A) = 2tan(A) / 1-tan²(A) so set this e...

Answered by Daniel M. • Maths tutor

3781 Views