Question 1071643
let P = internal pressuer
let D = internal diameter
let T = thickness
let S = stress
let K = constant of variation


variation formula would be:


S = K * P * D / T


you need to solve for K based on what you know and then you can use K to solve for what you don't know.


you know that:


S = 100 pounds per square inch when P = 25 pounds per square inch and D = 5 inches and T = .75 inches.


the variation formula of S = K * P * D / T becomes:


100 = K * 25 * 5 / .75


solve for K to get:


K = (100 * .75) / (25 * 5) = .6


now that you know the value of K, you can solve your problem.


you are given that:


P = 85
D = 9
T = .8


you know that K = .6.


since it is the constant of variation, it never changes, once it is originally determined for the particular problem on hand.


formula of S = K * P * D / T becomes:


S = .6 * 85 * 9 / .8


solve for S to get S = 573.75 pounds per square inch.


here's a reference on variation type problems and how to solve them.


<a href = "http://www.purplemath.com/modules/variatn.htm" target = "_blank">http://www.purplemath.com/modules/variatn.htm</a>