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The formula to find the cosine of the angle is: cosA= u.v/|u|x|v|; 1.u.v means that you multiply the x coordinates together, then the y coordinates and the z coordinates,...

Use laws of logarithms to simplify.Log₃((9y+b)/(2y-b)) = 2(9y+b)/(2y-b) = 3²(9y+b) = 9(2y-b)9y+b = 18y-9bCollect terms.9y = 10by = 10b/9

p=4pi² differentiating with respect to y we have dx/dy = 2(4y-sin2y)(4-2cos2y) substituting in the value of y =pi/2 we have dx/dy = 24pi, which means dy/dx =1/pi24using (y-y_1)=m(x-x_1) we have...

x = cos2θ  y = sinθcosθcos2θ = cos² θ  - sin²θ cos² θ  + sin²θ  = 12cos² θ  = 1 + cos2θ cos² θ  = 1/2(1 + x)2sin²θ  = 1 - cos...

This can be rewritten as x^1/2 + 4x^-1/2+ 4, hence dy/dx = (1/2)x^-1/2 - 2x^-3/2