Which term below correctly completes the following sentence?

Mathematics

2 answers:

Norma-Jean [14]3 years ago

3 0

Answer:

Step-by-step explanation:

Brrunno [24]3 years ago

3 0

Answer:

it d

Step-by-step explanation:

ap.ex

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Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 mill

abruzzese [7]

Answer:

V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year

Step-by-step explanation:

Given that oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 million barrels of oil in the well; six years later 1,500,000 barrels remain.

i.e. if V stands for volume of oil, then

$V' =kV\\dv/V= kdt\\ln V = kt+C\\V = Ae^{kt}$

To find A and k

V(0) = A = 3 million

Hence V = $3e^{kt}$

V(6) = 1.5

i.e. $1.5 = 3e^{6k}\\ln 1.5 =ln 3 +6k\\k = -0.11552$

$V(t) = 3e^{-0.11552t}$

a) Using the above value of k , we have

$V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794$ million per year.

4 0

3 years ago

Help me with this question please?

UNO [17]

$\bf 3^{n+2}-3^n=8\cdot 3^n\implies \boxed{3^n\cdot 3^2}-3^n=8\cdot 3^n
\\\\\\
\stackrel{common~factor}{3^n}(3^2-1)=8\cdot 3^n\implies 3^2-1=\cfrac{8\cdot \underline{3^n}}{\underline{3^n}}\implies 3^2-1=8
\\\\\\
9-1=8\implies 8=8$