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3 years ago

6

A squirrel in a tree drops an acorn. how long does it take the acorn to fall 52 feet?

1 answer:

Natali [406]3 years ago

4 0

2.43 seconds at the least

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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

Solve the system of equation using substitution. Show all of your work.

MrRa [10]

Answer:

x = 3

y = 6

Step-by-step explanation:

2x = x + 9

x = 3

y = 2 * 3

y = 6 . Hope this help teehee :D

5 0

3 years ago

HELP ASAP!!!! There is a clip below.

Ad libitum [116K]

Answer:

3.125

Step-by-step explanation:

We just multiply the dimensions together and when we do so we get 3.125.

4 0

3 years ago

The birdwatching club has 30 members, 21 girls and 9 boys. What is te ratio of girls to boys in the birdwatching club?

guapka [62]

30 members....21 girls and 9 boys

ratio of girls to boys is : 21/9 which reduces to 7/3 or 7:3 or 7 to 3

8 0

3 years ago

What is the image of (-4,-5) after a dilation by a scale factor of 3 centered at the origin?

prohojiy [21]

Answer:

I HOPE THIS HELPS I KINDA SUCK AT MATH

Step-by-step explanation:

B': (-12,15)

Step-by-step explanation:

B': (3×-4, 3×5)

B': (-12,15)

7 0

3 years ago