Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse with sides parallel to the coordinate axes.

6. sarah saved $12.75 every week for a number of weeks, w. she received an additional $25 during the last week in which she saved money. write and solve an equation to find the number of weeks, w, for which sarah had saved money if she has $114.25 now.