Search over 10,000 free study notes

First of all, we need to express tangent and cotangent in terms of sine and cosine using the identities: tanx = sinx / cosx and cotx = cosx / sinx. Substituting these expressions into the initial equation...

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2],=[x(3x-2)]/[(3x-1)^2]

y = x³ - 3x² - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x² - 6x -24 = 0 -> x² - 2x - 8 = 0 -> (x+2)(x-4) = 0Th...

Sphere A has mass m and velocity +3v so its initial momentum is 3mv. Sphere B has mass 2m and velocity -v so its initial momentum is -2mv. Therefore we can say:3mv - 2mv = M_cv_c, wher...

Conservation Laws are useful because they establish fixed rules that physical interactions must follow, which helps physicists to better understand these processes. In particular, they provide a picture o...