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Mathematics

1 answer:

Mashutka [201]3 years ago

5 0

Answer:

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Step-by-step explanation:

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The cost of building a new house is directly proportional to the number of square feet in the house. If a 1,500-square-foot hous

bezimeni [28]

If you divide 120,000 by 1,500 you will get the amount that it costs per square feet which you would then multiply by 2,400 to get 192,000. So the answer is $192,000

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A certain country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The

mash [69]

Answer:

$\bf x(t)=10(1-e^{-0.005*t})$

Step-by-step explanation:

The differential equation

$\bf \displaystyle\frac{dx}{dt}=0.005(10-x)$

can be solved by separation of variables. Write the equation as

$\bf \displaystyle\frac{dx}{10-x}=0.005dt$

Integrate on both sides

$\bf \int\displaystyle\frac{dx}{10-x}=\int0.005dt\Rightarrow -ln(10-x)=0.005t+C\Rightarrow\\\\\Rightarrow ln(10-x)^{-1}=0.005t+C\Rightarrow (10-x)^{-1}=e^{0.005t}e^C$

where C is a constant.

$\bf e^C$ is also a constant and we will keep calling it C, (there is no reason to change the letter). We have then

$\bf (10-x)^{-1}=Ce^{0.005t}\Rightarrow \displaystyle\frac{1}{10-x}=Ce^{0.005t}\Rightarrow 10-x=\displaystyle\frac{1}{Ce^{0.005t}}\Rightarrow\\\\\Rightarrow x(t)=10-(1/C)e{-0.005t}$