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Work out the lengths of each side; do so by adding the ratio components together (3+4+5).The components add to 12; we can now find the value of a single unit of the ratio, by dividing 72 by 12.72/12 is 6;...

The stationary point on the curve is the point on the curve where the gradient is 0. In other words the tangent to the curve at that point is horizontal. The gradient of the curve can be expressed as dy/d...

Route 1 (Standard): 1. 3x + y = -4 / 2. 3x - 4y = 6 / MINUS 2 FROM 1 / y - (-4y) = 5y / -4 - 6 = - 10 / 5y = - 10 / y = -2 /PUT y-VALUE BACK INTO ORIGINAL EQ  / 3x - 2 = -4 / 3x = ...

First, we want to convert the equation to a simpler form involving just one function of x. Squared trigonometric functions are normally good candidates for simplification, thanks to the trigonometric iden...

Answer: sin^3(x)/3 + c
The student can either solve by inspection by noticing that the derivative of sin^3(x)=3sin^2(x)cos(x).
OR
The student can use the longer method of integration by par...