Answer:
a = 4.762203156
Step-by-step explanation:
Given:
ab^4 = 12 and a^5b^5 = 7776
Making the equations a subject of a;
a = 12/b^4 and a^5 = 7776/b^5
Finding fifth root on both sides of equation two;
a = /b
You will get a = 6/b
Equating the two equations;
12/b^4 = 6/b
Multiplying both sides by b^4 gives:
b = = 1.25992105
We had that a = 12/b^4 so;
a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156
Answer:
Step-by-step explanation:
The easier way to figure this is by using the concept of torque in physics. If the torque of the man is greater than that experienced by the box, the lever will tilt in the man's favor (in other words, he will move down and the box will be lifted). Torque is found by multiplying the perpendicular force by the length of the lever arm. Because we want the man's torque to be greater than the box's torque, the inequality is:
and
That decimal is 6 inches in terms of meters.
180r > 76.2 so
r > .42 meters or `16.67 inches. The man has to sit at a distance greater than 16.67 inches in order for the box to be lifted by the lever.