All categories

2 years ago

4/9 - 2/5 give answer in its simpliest form

Mathematics

1 answer:

wlad13 [49]2 years ago

8 0

Answer:

2/45 is your answer

You might be interested in

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

Solve the formula V=pir^2h for r <br><br> PLEAASSSEEE HELP

otez555 [7]

Answer:

Step-by-step explanation:

So we have the formula:

$V=\pi r^2h$

And we want to solve it for r.

So, let's first divide both sides by π and h. This will cancel out the right side:

$r^2=\frac{V}{\pi h}$

Now, take the square root of both sides:

$r=\sqrt{\frac{V}{\pi h}}$

And we're done!

Our answer is B.

I hope this helps!

7 0

3 years ago

Read 2 more answers

-6(y + 15) = -3y + 6 what is the value of y

Serga [27]

Let's begin by listing out the information given to us:

$-6\mleft(y+15\mright)=-3y+6$

We are to find the value of y

$undefined$

6 0

10 months ago

33.366 divided by 6.7

andrey2020 [161]

Answer:

Step-by-step explanation:

33.366/6.7= 4.98

5 0

3 years ago

What kind of sequence has a common ratio

Makovka662 [10]

Answer:

geometric sequence

Step-by-step explanation:

A geometric sequence is a sequence of numbers that is ordered with a specific pattern. Each successive number is the product of the previous number and a constant. The constant is the same for every term in the sequence and is called the common ratio.

6 0

2 years ago