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i is the unit vector (magnitude of 1) in the direction of the positive x-axis. j is the unit vector in the direction of the positive y-axis. The magnitude of F would be the length of ...

(There is a diagram showing a rectangle with one side labelled x+4 and another labelled x+6)Area = (x+4)(x+6)63m^2 = x²+10x+240 = x²+10x-390 = (x-3)(x+13)
x-3=0 so x=3x+13=0 giv...

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...