Mathematics OpenStudy (anonymous):

Suppose a mothball loses volume at a rate proportional to its SURFACE AREA. If the radius of the ball decreases from 2cm to 1cm in 2 months, how long will it take till the radius is 1 mm? OpenStudy (dumbcow):

$\frac{dV}{dt} = k(4 \pi r^{2})$ $\frac{dV}{dt} = \frac{dV}{dr}*\frac{dr}{dt}$ $\frac{dV}{dr} = 4 \pi r^{2}$ $\rightarrow (4 \pi r^{2})\frac{dr}{dt} = k(4 \pi r^{2})$ $\frac{dr}{dt} = k \rightarrow dr =k*dt$ $\int\limits_{}^{}dr = \int\limits_{}^{} k dt$ $r = kt + C$ $r(0) = 2 \rightarrow C = 2$ $r(2) = 1$ $1 = 2k +2$ $\rightarrow k = -\frac{1}{2}$ $r = -\frac{1}{2}t +2 = \frac{1}{10}$ $t = \frac{19}{5} = 3.8 months$

Latest Questions anikareddy: mitchells family is cooking 2 3/4 pounds of meat. the recipe says to cook the mea
17 seconds ago 0 Replies 0 Medals DiscordTv: @vocaloid @vocaloid @vocaloid @vocaloid @vocaloid @vocaloid @vocaloid @vocaloid @
6 seconds ago 8 Replies 0 Medals heychelle: Which phrase makes it clear that Roosevelt is aiming his argument at journalists? "the body politic, economic and social" "every evil man whether politician
4 minutes ago 0 Replies 0 Medals AriahMHebrank: Which mountain range is marked with the letter D? Rocky Mountains Cascade Mountai
6 seconds ago 17 Replies 0 Medals 100kpimpcess: help ss below
19 seconds ago 17 Replies 1 Medal 100kpimpcess: kan a mod or sum close my math question
12 minutes ago 3 Replies 2 Medals BrandonKeele: I need help finding the circumference, I have my notes, and all that, but Idk- I'm just slow when it comes to math, I just don't understand it, also my teac
16 minutes ago 10 Replies 4 Medals kekeman: Math: https://snipboard.io/2Y1zog.jpg
4 minutes ago 11 Replies 2 Medals snowflake0531: @florisalreadytaken
7 minutes ago 8 Replies 0 Medals Anaise: Ok. Not a question. Just a sloppy take. I don't study psychology, nor am I the most articulate.
33 minutes ago 2 Replies 4 Medals