Madison is organizing her bookshelf. she places her favorite book on the first shelf. she puts 2 books on the second shelf and 4 books on the third shelf. she continues by putting 8 books on the fourth shelf and 16 books on the fifth shelf. she has one more shelf left. if this pattern continues, how many books will be on the last shelf? explain how you found your answer.

The perimiter of a rectangle is 70 inches the legneth of the rectangle is 5 less than 3 times the width of the rectangle what is the width of the rectangle

To find the extreme values of a function f(x. y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x, y)=xy

Determine which expressions represent real numbers and which expressions represent complex number. asaaap! plis!