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Setting the two equations equal to one another to find the intersection boundaries:x^2+16x+4=6x+4; x^2+16x+4-6x-4=0; x^2+10x=0;x(x+10)=0; x=0, x=-10. Setting up the vol...

Isolate the 'ln term'
2ln(2x+1) = 10ln(2x+1) = 5
Take to the exponential power form
e^(ln(2x+1)) = e^52x+1 = e^5
Simplify
2x = e^5 -1x = (e^5-1)/2

This question is assessing your knowledge of units and their conversion. Notice that the area units of the roll of card and the postcard are different, so it is important that before we carry out any calc...

The most important fact to remember with this question is that two perpendicular straight lines have gradients related by m₁ = -1/m_2. This can then be used to find the gradient of t...

The equation is of the formx²+bx+c=0This means it can be rearranged to(x+(b/2))²=(b/2)²-cTaking the square root of both sides leaves us with x.
x²-12x-45=0...