1. How are systems of equations used in the real world? Help me plzzzz

Mathematics

1 answer:

nadezda [96]3 years ago

8 0

Answer:

Systems of linear equations are used in the real world by economists and entrepreneurs to find out when supply equals demand.It's all about the mullah, and if you don't know the numbers when you have a business, it might fail.

Step-by-step explanation:

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A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into t

nignag [31]

If $A(t)$ is the amount of salt in the tank at time $t$ , then the rate at which the amount of salt in the tank changes is given by

$\dfrac{\mathrm dA(t)}{\mathrm dt}=\dfrac{4\text{ lbs}}{1\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}-\dfrac{A(t)\text{ lbs}}{600\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}$
$\dfrac{\mathrm dA}{\mathrm dt}=24\dfrac{\text{lb}}{\text{min}}-\dfrac{A(t)}{100}\dfrac{\text{lb}}{\text{min}}$

Let's drop the units for now. We have

$\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{A(t)}{100}=24$
$e^{t/100}\dfrac{\mathrm dA(t)}{\mathrm dt}+e^{t/100}\dfrac{A(t)}{100}=24e^{t/100}$
$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/100}A(t)\right]=24e^{t/100}$
$e^{t/100}A(t)=\displaystyle24\int e^{t/100}\,\mathrm dt$
$e^{t/100}A(t)=2400e^{t/100}+C$
$A(t)=2400+Ce^{-t/100}$

We're given that the water is pure at the start, so $A(0)=0$ , giving

$A(0)=0=2400+Ce^{-0/100}\implies C=-2400$

So the amount of salt in the tank (in lbs) at time $t$ is

$A(t)=2400\left(1-e^{-t/100}\right)$

4 0

2 years ago

Write an equation of the ellipse centered at the origin given its vertex and co vertex

jolli1 [7]

Answer:

$\dfrac{x^2}{49}+\dfrac{y^2}{25}=1.$