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1. In circular motion F = mv²/rPlug numbers in ... 6 = 0.4* v² / 0.6 ... and rearrange for v = plus or minus 3. Velocity is a vector so it doesn't matter which value you take as i...

You can see that this question is asking you to do integration by parts. Remember that the integral of uv' is equal to uv - the integral of u'v. You want to find a u that gets easier when you differentiat...

(using double angle formula)Sin^2(x)=1/2-(Cos(2x)/2)
So the Integral is 1/2(x-1/2Sin(2x))which simplifies to x/2 - 1/2Sin(x)Cos(x)

Firstly, we need to express 6cos(2x) + sin(x) in terms of sin(x) 6cos(2x) + sin(x) = 6cos(x+x) + sin(x) = 6cos²(x) - 6sin²(x) + sin(x) (applying cos(x+y) = cos(x)cos(y) - sin(x)sin(y...

x² +2xy–3y²+16=0Differentiate the terms:x² gives 2x2xy is differentiated by the product rule: vu' +v'u Make v = 2x and u = y, which gives 2x(dy/dx) + 2y3y² give...