Concern of the angle of approach was raised, so a simple multiplier was added to the front of the x-component. also a rotation of the axes allows for a more accurate representation of the satellite's path. r= , where 0 = angle of rotation set 8 = tt/4, find the curvature k when a = 12, a = 1, and a = 2. is there an easier way to find the curvature than using the large parametric function? does the value of change the curvature at all?

A75-hp (shaft output) motor that has an efficiency of 91.0 percent is worn out and is to be replaced by a high-efficiency motor that has an efficiency of 95.4 percent. the motor operates 4368 hours a year at a load factor of 0.75. taking the cost of electricity to be $0.12/kwh, determine the amount of energy and money saved as a result of installing the high-efficiency motor instead of the standard motor. also, determine the simple payback period if the pu