Search over 10,000 free study notes

The forces should be resolved in two directions: parallel to the plane, and perpendicular to the plane. Friction will act parallel to the plane (up the slope), and the normal force wil act perpendicular t...

sin(60◦) = √3 /2 

tan(60◦) = √3

6sin(60◦) + 5tan(60◦) = 3√3 + 5√3 = 8√3 = √64√3 = √192

First substiute sin(theta) = x (This step is not nesecessary but often people find quadratics easier to solve in variables that they usually use). Then due to the fact that the "b" coefficient i...

Let's first recall the definition of tan(x) = sin(x)/cos(x). Hence, y' = d/dx( sin(x)/cos(x) ). Recall quotient rule for differentiation: ( f(x)/g(x) )' = ( f '(x)^2*g(x) - f(x)*g'(x)^2 ) / g(x)^2 and tha...

x²-2x+4= (x-2)(x-2)=0  x=-2 (double root)  

x²+5x+1=0

x_1,2= -5+_ (5²-4(1)(1) )^0.5/2 

x₁=4.8     x₂=-0.2 (t...