10. a weight hangs on a spring. the vibration period of that weight is the time in which it makes a complete cycle in motion. suppose the relationship between the vibration period "t" (in seconds) and the weight "w" (in kilograms) is given by t = 2 √(w / 200). find the period t for a spring with a hanging weight of 2.0 kilograms.

The vibration period of the spring will be 0.2 seconds

Explanation

The relationship between the vibration period "T" (in seconds) and the weight "w" (in kilograms) is given by...

Given that, the weight(w) = 2.0 kilograms

So, plugging w = 2.0 into the above equation, we will get...

So, the vibration period of the spring will be 0.2 seconds.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: