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Firstly, let's split the equation "xcosx" into two parts to integrate them separately. 1) Let u=x and dv/dx=cosx 2)As the integral of x is 1, du/dx=1 3)To find v, we integrate cosx to get v=sinx...

In maths when we are asked to re express something we really only have 2 tricks. Multiply by 1, or add Zero. The hard part is finding how to express 1 or zero to suit the problem. For this one we should m...

Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can i...

We approach this problem using the conservation of linear momentum, which tells us that m1 x v1 = m2 x v2. We substitute the values of m1, v1 and v2, and solve for m2: 48x1.2=m2x16; m2=57.6/16=3.6 kg.

Answering this question requires knowledge of e and ln. If we look at the question we can see 2 is being multiplied by the ln, so we might want to use the product rule. Also, we can see that the ln has a ...