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3 years ago

6

On Monday, water was pumped out of the pool at a constant rate, starting at 12:00 p.m.

2 answers:

Talja [164]3 years ago

5 0

Answer:

so every 20 minutes it goes down by 4 inches so 20x-4y

Step-by-step explanation:

20x-4y means every 20 minutes it goes down 4 inches

i just did this for someone lol

cupoosta [38]3 years ago

3 0

Answer: Every ten minutes the water decreases by two, so you would divide 2/10, which would be 0.2, meaning the water decreases 0.2 inches per minute.

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A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into t

Gwar [14]

Answer:

(a) $A = 1500(1 - e^{-0.01t})$

(b) $t = 0$

Step-by-step explanation:

Given

$V= 300gal$ --- Volume of tank

$B = 5lb/gal$ --- Brine solution

$R_1 = 3gal/min$ --- Rate in, in gallon/min

$R_2 = 6gal/min$ --- Rate out, in gallon/min

Required

Determine A(t)

First, calculate the rate in (R in) and (R out) in lb/min

$R_{in} = B * R_1$

$R_{in} = 5lb/gal * 3gal/min$

$R_{in} = 15lb/min$

R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2

So, we have:

$R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min$

$R_{out} = \frac{3*A(t)}{300} lb/min$

$R_{out} = \frac{A(t)}{100} lb/min$

The change in the amount of brin e in the tank at time t is given as:

$A'(t) = R_{in} - R_{out}$

$A'(t) = 15 - \frac{A(t)}{100}$

Rewrite:

$\frac{dA}{dt} = 15 - \frac{A}{100}$

Multiply through by dt

$dA = [15 - \frac{A}{100}]* dt$

Make dt stand alone

$\frac{dA}{15 - \frac{A}{100}} = dt$

$ln|15 - \frac{A}{100}| = -0.01t + ln\ c$

Express as exponents

$15 - \frac{A}{100} = ce^{-\frac{t}{100}}$

Multiply through by 100

$1500 - A = 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-0.01t}$

Apply initial conditions

$A(0) = 0$

Substitute 0 for t in: $A = 1500 - 100ce^{-0.01t}$

$0 = 1500 - 100ce^{-0.01*0}$

$0 = 1500 - 100ce^{0}$

$0 = 1500 - 100c$

$100c = 1500$

$c = 15$

Substitute 15 for c in $A = 1500 - 100ce^{-0.01t}$

$A = 1500 - 100*15e^{-0.01t}$

$A = 1500 - 1500e^{-0.01t}$

Factorize:

$A = 1500(1 - e^{-0.01t})$

How long to empty the tank

Set A to 0

$1500(1 - e^{-0.01t}) = 0$

Divide through by 1500

$1 - e^{-0.01t} = 0$

Collect Like Terms

$e^{-0.01t} = 1$

Take ln of both sides

$ln\ (e^{-0.01t}) = ln\ 1$

$-0.0t = 0$

$t = 0$

8 0

3 years ago

kaitlin is on a long car trip every time she stops she loses 15 minutes of travel time is she stops 5 times how late will she be

yanalaym [24]

5(15)= 75 minutes or an hour and 15 minutes lost

8 0

4 years ago

Read 2 more answers

in an isosceles right triangle the hypotenuse is 8.4 in find the length of a side to the nearest tenth of an inch

Mamont248 [21]

<span><span>a2</span>+<span>a2</span>=<span>8.42</span></span>

<span>2<span>a2</span>=<span>8.42</span></span>

<span><span>a2</span>=<span><span><span>(8.4)</span>2</span>2</span></span>

<span><span>a2</span>=<span>70.562</span></span>

<span><span>a2</span>=35.28</span>

<span>a≈<span>5.9</span></span>

5 0

4 years ago

Read 2 more answers

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inc

V125BC [204]

Answer:

Answer: the volume of the cylinder is 1.5 more than the cone

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What is (4x6) x (3-2)

Iteru [2.4K]

Answer: 24

Step-by-step explanation: do 4 times 6 first then 3-2 and then times it and you get 24

5 0

3 years ago