3 years ago

This probability distribution shows the

Mathematics

1 answer:

-Dominant- [34]3 years ago

8 0

Answer:

Answer is 0.14.

Step-by-step explanation:

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What is 3,264 in expanded notation

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Jackson's grandmother is moving to a new house. Grandmother has eighty-seven boxes for Jackson to put in the truck. Jackson puts

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I need help with this one please

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plot $30 on the line above one and plot $50 on the line above two and keep doing the same thing

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Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at

DiKsa [7]

Salt flows in at a rate of (5 g/L)*(3 L/min) = 15 g/min.

Salt flows out at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

So the net flow rate of salt, given by $x(t)$ in grams, is governed by the differential equation,

$x'(t)=15-\dfrac{3x(t)}{10}$

which is linear. Move the $x$ term to the right side, then multiply both sides by $e^{3t/10}$ :

$e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}$

$\implies\left(e^{3t/10}x\right)'=15e^{3t/10}$

Integrate both sides, then solve for $x$ :

$e^{3t/10}x=50e^{3t/10}+C$

$\implies x(t)=50+Ce^{-3t/10}$

Since the tank starts with 5 g of salt at time $t=0$ , we have

$5=50+C\implies C=-45$

$\implies\boxed{x(t)=50-45e^{-3t/10}}$

The time it takes for the tank to hold 20 g of salt is $t$ such that

$20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}$

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