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Ierofanga [76]
2 years ago
11

The ratio of red to greens was 5 to 16 and six times the number of reds exceeded the number of greens by 112. How many were red

and how many were green?
Mathematics
1 answer:
s2008m [1.1K]2 years ago
3 0
<span>Red is 'R' while Green is "G" </span>
<span>from the ratio, 5R = 16 G </span>
<span>and the second equation is 6R = G +112 </span>
<span>Lets solve for G in the 2nd equation ----> G = 6R -112 </span>
<span>Plug the G value into the first equation ----> 5R = 16(6R -112) -->R = 19.69 </span>
<span>Plug the R value into the second equation to get G-----> G = 6.14</span>
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<h2>MEAN</h2>

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Answer:

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\frac{dy}{dt} =ky(1-y)

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Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

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Differential equation

\frac{dy}{dt} =ky(1-y)

Solving the differential equation

\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}

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y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

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The rumor reaches 80% at 8.48 days.

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