Mathematics: Easy questionwater flows continuously froma large tank at a rate proportional to the amount of water remaining; that is, dy/dt=ky. ther was initially 1 cubic feet of water in the tank. at t=4 hours, 8000 cubic feet of water remained, what is k in dy/dt=ky? show all work

Easy questionwater flows continuously froma large

Ответ:

Kekkdkskdkdk

04.01.2022

$\dfrac{\mathrm dy}{\mathrm dt}=ky\iff\dfrac{\mathrm dy}y=k\,\mathrm dt$

Integrating both sides, we get

$\ln|y|=kt+C$
$\implies y=e^{kt+C}=e^{kt}e^C=Ce^{kt}$

When t=0

, we have

, so that

$10000=Ce^{0k}\implies C=10000$

When t=4

, we have

, which means

$8000=10000e^{4k}\implies k=\dfrac14\ln\dfrac{8000}{10000}\approx-0.0558$

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Ответ:

tylerchitwood211

29.10.2020

Mathematics

Step-by-step explanation:

add me on snap and ill show you ;)

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Easy question
water flows continuously froma large tank at a rate proportional to the amount of water remaining; that is, dy/dt=ky. ther was initially 1 cubic feet of water in the tank. at t=4 hours, 8000 cubic feet of water remained, what is k in dy/dt=ky?

show all work

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