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This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively strait...

x=1, y=3; Firstly, rearranging for x in the first equation: x = (7-2y); Substitute this into the second equation: 3y - (7 -2y) = 8; Expand: 3y -7 +2y = 8 (watch negative) 3y +2y = 15 Therefore, 5y = 15 an...

Step 1: Draw a labelled diagram of the triangle, marking the side lengths. Step 2: Recall Pythagoras’ theorem equation ‘c2=a2+b2’ Step 3: Substitute the values of a and b into the equation. c2=8.652+10.15...

I believe that there is no better way to revise for Maths than to continually practice questions (especially those that you find most tricky!) The more you practise, the easier you'll find the questions b...

Step 1: Eliminate the ‘y’ component from the equations by adding the equations together. This gives the new equation ‘6x=12’

Step 2: Find the value of x by dividing both sides of the equation by 6....