Consider the boundary-value problem introduced in the construction of the mathematical model for the shape of a rotating string: . For constant T and r, define the critical speeds of angular rotation vn as the values of v for which the boundaryvalue problem has nontrivial solutions. Find the critical speeds vn and the corresponding deflections yn(x).

9/27/2016 MATH 220 Watson Notes I. Correlation coefficient = r a. Coefficient of determination i. % of the change in y can be explained by the linear relationship between‘x’ and ‘y’ 1. Tells you weak, moderate strong 2. Tells you how much you know 3. How much you don’t know ii. REMEMBER WORD FOR WORD II. Interpret Slope a. M= y2- y1/x2-x1 i. Change in y over change inx 1. What if we let x change 1 unit a. Then slope is reallyhow y is changing ii. As x increases or decreasesone unit, y increases or decreasesslope