Solve for n. 121 Y 6 Z F 2.5 7.5 H X m2 15 G

Mathematics

1 answer:

Dafna11 [192]3 years ago

6 0

Answer:

n = 18

Step-by-step explanation:

Corresponding parts of similar triangles are in same ratio

$\frac{FG}{XY}=\frac{HG}{YZ}\\\\\frac{n}{6}=\frac{15}{5}\\\\n=\frac{15}{5}*6\\\\n=3*6\\\\n=18$

You might be interested in

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

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

We're given that after 10 years, 99.97% of the original amount of uranium remains. This means (if $t$ is taken to be in years) for some starting amount $u$ ,

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