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dimulka [17.4K]

4 years ago

5

Order is important in a two-column proof. True False

1 answer:

NARA [144]4 years ago

5 0

Yes order is important

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Solve Using Dirac Deltla/discontinuous forcing

Jet001 [13]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're told that $A(0)=0$ .

For $0\le t\le15$ , the salt flows in at a rate of (1/5 lb/gal)*(5 gal/min) = 1 lb/min. When the regulating mechanism fails, 20 lbs of salt is dumped and no more salt flows for $t>15$ . We can capture this in terms of the unit step function $u(t)$ and Dirac delta function $\delta(t)$ as

$\text{rate in}=u(t)-u(t-15)+20\delta(t-15)$

(in lb/min)

The salt from the mixed solution flows out at a rate of

$\text{rate out}=\left(\dfrac{A(t)\,\mathrm{lb}}{50+(5-5)t\,\mathrm{gal}}\right)\left(5\dfrac{\rm gal}{\rm min}\right)=\dfrac A{10}\dfrac{\rm lb}{\rm min}$

Then the amount of salt in the tank at time $t$ changes according to

$\dfrac{\mathrm dA}{\mathrm dt}=u(t)-u(t-15)+20\delta(t-15)-\dfrac A{10}$

Let $\hat A(s)$ denote the Laplace transform of $A(t)$ , $\hat A(s)=\mathcal L_s\{A(t)\}$ . Take the transform of both sides to get

$s\hat A(s)-A(0)=\dfrac1s-\dfrac{e^{-15s}}s+20e^{-15s}-\dfrac1{10}\hat A(s)$

Solve for $\hat A(s)$ , then take the inverse of both sides.

$\hat A(s)=\dfrac{\frac{10-10e^{-15s}}{s^2}+\frac{200e^{-15s}}s}{10s+1}$

$\implies\boxed{A(t)=10-10e^{-t/10}+\left(30e^{3/2-t/10}-10\right)u(t-15)}$

7 0

4 years ago

California has a land area of 163,676 mi2 and a population of 39.51 million people. Find the population density of California to

guajiro [1.7K]

Answer:

(A)241.4 people per mi²

Step-by-step explanation:

California's Population=39.51 million=39,510,000

California's Land Area=163,676 mi²

Population Density=Population ÷Area

=39,510,000÷163,676

=241.39

≈241.4 people per mi² (correct to the nearest tenth)

5 0

3 years ago

A family purchased tickets for a concert. They paid a total of $90 for 7 adult tickets and 12 child tickets. The price of a chil

Anit [1.1K]

Answer: 7 + 2/3(12) = 15

90/15 = $6 for adult tickets

7 0

3 years ago

I did my work I just didn’t show it. But is the answer 2 5/6? This is not improper fraction it is subtracting Fractions (with re

Advocard [28]

yes you are correct

8 0

3 years ago

The sum of two number is 45.if one of them is 27 ,find another

tekilochka [14]

Answer:

is 18

Step-by-step explanation:

simple you just subtract 27 for the original number

8 0

3 years ago

Read 2 more answers