The formula \( D=50 e^{-0.4 h} \) can be used to find the number of milligrams \( D \) of a certain drug that is in a patient's bloodstream \( h \) hours after the drug was administered. When the number of milligrams reaches 3 , the drug is to be administered again. What is the time between injections? The time between injections is (Round to two decimal places as needed.).

\( \int _ { - 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 14 - y ^ { 2 } } } \int _ { - \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } } y ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d z d x d y \)

Calcular el área de las siguientes regiones que están delimitadas por las siguientes curvas cuyas ecuaciones son: A) \( \mathrm{y}^{2}=-\mathrm{x} \quad ; \mathrm{x}-\mathrm{y}=4 \quad ; \mathrm{y}=-1 \quad ; \mathrm{y}=2 \)

\( \int 2 \cot x + \sec ^ { 2 } x = 0 , \quad 0 \leq x \leq 2 \pi \)

A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 3 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.

Calcular el área de las siguientes regiones que están delimitadas por las siguientes curvas cuyas ecuaciones son: A) \( y=x^{3} \quad ; \quad y=2 x-x^{2} \)