Question

1. Use the Law of Levers to solve the problem, x1y1=x2y2.

Answer 1

1)  Never heard of someone referring to the Law of Levers before, must be showing my age.  A system as you describe is at equilibrium when the net torque is equal to zero. Since torque is Fr=mgr so for this system we have a sum of:

27g*10+30g*x=0  The sum must be zero to be at equilibrium, dividing both sides by g you have:

270+30x=0

270=-30x

x=-9

The negative just indicates that the magnitude of 9 is on the opposite side of the fulcrum, so x=9ft in magnitude.

2)  Inverse variation is of the form y=k/x, in this case we are given a point so we can solve for the constant, k, of variation...

y=k/x, and we are given y=-12 when x=5 so

-12=k/5

k=-60  so the equation is:

y=-60/x which can be expressed as

xy=-60