Problem:
consider a particle with initial velocity v⃗ that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis.

what is the x component vx of v⃗ in meters per second?

Example:

Suppose that a ball has an initial velocity v0 that has magnitude 20.0 m/s and is directed 60.0 degrees above the negative x axis.

Then, the x-component is,
20.0 * cos(-60) = 20.0 * (1/2) = 10.0 m/s

If the heat engine is a perfect carnot cycle engine, thenefficiency = (t2-t1)/t2   where t1=temperature of cold reservoir ( ° k) = 135            t2=temperature of hot reservoir ( ° k)   = 325thereforeefficiency = (t2-t1)/t2 = (325-135)/325 = 0.5846 = 58%  note: this is the theoretical maximum efficiency of a perfect heat engine.   real-life engines do not achieve this value.