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ehidna [41]
4 years ago
7

What authority does the legislative branch have over the courts?

Mathematics
1 answer:
Snowcat [4.5K]4 years ago
8 0
Legislative=makes laws
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4 years ago
A contaminant is leaking into a lake at a rate of R(t) = 1700e^0.06t gal/h. Enzymes that neutralize the contaminant have been ad
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16,460 gallons

Step-by-step explanation:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be:

\frac{dQ}{dt} =1700exp(0.06t)*exp(-0.32t)\\\frac{dQ}{dt} =1700exp(-0.26t)\\

Then, we have to integrate in order to find the equation for Q(t), as the quantity of contaminant in the lake, in function of time.

\int\limits^0_t {dQ}=\int\limits^0_t {1700exp(-0.26t)dt}\\Q(t)=\frac{1700}{-0.26} exp(-0.26t)+C \\

Now, we use the given conditions to replace them in the equation, in order to solve for C

t_{0} =0\\Q_{0}=10,000\\Q_{0}=-6538exp(-0.26*0)+C\\C=10,000+6538=16538

Then, we reorganize the equation and we replace t for 17 hours, in order to determine the quantity of contaminant at that time:

Q_{t} =-6538exp(-0.26t)+16538\\Q_{17} =-6538exp(-0.26*17)+16538\\Q_{17} =16460 gallons

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3 years ago
Simplify the variable expression below as much as possible.<br> 8x + 4 + 8x-1
vampirchik [111]
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