Pearl drove 90 miles and used 5 gallons of gas. Lourdes used 2 gallons of gas to drive 48 miles.

Mathematics

1 answer:

andrew11 [14]3 years ago

6 0

Hello there!

Pearl drives 18 Miles with every 1 gallons of gas, Lourdes Drives 24 miles every 1 gallons of gas. Lourdes is using less gas and driving more miles than Pearl every gallon so he is using gas more efficiently.

Hope this helped!!

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A breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount of uranium-238 pres

topjm [15]

Let $U(t)$ denote the amount of uranium-238 in the reactor at time $t$ . As conversion to plutonium-239 occurs, the amount of uranium will decrease, so the conversion rate is negative. Because the rate is proportional to the current amount of uranium, we have

$\dfrac{\mathrm dU}{\mathrm dt}=-kU$

where $k>0$ is constant. Separating variables and integrating both sides gives

$\dfrac{\mathrm dU}U=-k\,\mathrm dt\implies\ln|U|=-kt+C\implies U=Ce^{-kt}$

Suppose we start some amount $u$ . This means that at time $t=0$ we have $U(0)=u$ , so that

$u=Ce^{-0k}\implies C=u\implies U=ue^{-kt}$

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$0.9997u=ue^{-10k}\implies k=-\dfrac{\ln(0.9997)}{10}$