Physics, 31.10.2019 01:31 coronadohayden

400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. the volume of the lake including the pesticide is 108 gallons. a river flows into the lake bringing 5,000 gallons of fresh water per minute, and the uniform mixture spills over the dam at the same rate. how long, in minutes, will it take to reduce the pesticide in the lake to a safe level of 1 part per million gallons? (round your answer to the nearest minute.

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Answer from: monica1400

t=27725.8minutes

Explanation:

To determinate use the law the change of volume in determinate time is derivate so:

$\frac{dV}{dt}=flowin-flowout$

The flow in is zero and the flow out is modeling with V as the volume out in the volume of the lake in the reason of change.

$\frac{dV}{dt}=0-(\frac{V}{10x10^{8}})*5000\\\frac{dV}{dt}=-5x10^{-5}*V \\dV*V=-5x10^{-5}*dt$

Integrate to get the volume function

$\int\limits{\frac{1}{V}}\, dv=\int\limits{-5x10^{-5} }\, dt\\ ln(V)=-5x10^{-5}*t\\ln*e(V)=C*e^{-5x10^{-5}*t}\\$

The find the constant C in the time t=0 the volume is knowing so:

$t=0s\\V=400\\V=C*e^{0}\\C=400$

$V=400*e^{-5x10^{-5}*t}$

The volume is 1 part per million so:

$\frac{V}{10x^{8}}=\frac{1}{10x^{6}}\\ V=100$

$V=400*e^{-5x10^{-5}*t}\\100=400*e^{-5x10^{-5}*t}\\\frac{100}{400}=e^{-5x10^{-5}*t}\\ln*\frac{1}{4}=ln*e^{-5x10^{-5}*t}\\-ln(4)=-5x10^{-5}*t\\ t=\frac{-ln(4)}{-5x10^{-5}}=27725.88\\t=27725.8minutes$

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

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