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Firstly, you should change the equation into the form y=mx+c where m is the gradient and c is the y-intercept. This can be done by subtracting 3x from each side of the equation to give 5y=-3x+7. Then divi...
the curve crosses the graph at the x axis at 0.5,3 and -4 so f(0.5)=0, f(3)=0,f(-4)=0. All linear factors are the form of g(x)=(x-a) so 0=g(0.5)=0.5-a. rearranging we get that a=0.5 ie g(x)=x-0.5 similarl...
Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+...
Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is...
The island is 2km. If the scale is 1cm:500m we need to multiply both left and right sides by 4 to get to the 4cm that was measured. This gets us 4cm: 2000m . We now need to convert 2000m to km which gives...
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