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3 years ago

What is 7 1/5 written as a percent

Mathematics

1 answer:

Alla [95]3 years ago

5 0

7.20% percent I think

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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

Which number is between 7.17 x 10^4 and 8.17 10^5 A. 6.92 x 10^4 B. 7.2 x10^9 C. 7.57 x 10^3 D. 8.053 x 10^4

Serga [27]

Answer:

D. 8.053 x 10^4

Step-by-step explanation:

Given :

7.17 x 10^4 and 8.17 10^5

The number in between the two Given numbers should be greater Than 7.17*10^4 but less than 8.17*10^5

A. 6.92 x 10^4 - this is less than 7.17 * 10^4 ; hence doesn't fit in

B. 7.2 x10^9 - this is greater than both values, hence, doesn't fit in

C. 7.57 x 10^3 - this is less than 7.17*10^4 ; hence does not fit in

D. 8.053 x 10^4 - this fits in as it is greater than 7.17*10^4 and less than 8.17*10^5 ; hence, it is the correct answer.

6 0

3 years ago

Solve the following inequality: 10t + 7 , 200 > 21 , 000

Alla [95]

Answer:

t > 1380

Step-by-step explanation:

Subtract 7200 from both sides

10t + 7200 - 7200 > 21000 - 7200

Simplify

10t > 13800

Divide both sides by 10

10t/10 > 13800/10

Simplify

t > 1380

4 0

3 years ago

Drag the coordinates to match the coordinates of each point on the left with the coordinates of its reflection across the x-axis

fredd [130]

Answer:

1. (-2,-7)

2. (3,-9)

3. (7,-2)

4.(-3,9)

Step-by-step explanation:

Since the reflection is across the x-axis, the y-coordinate will be flipped.

Example: (-7,4) would become (-7,-4)

HOWEVER, if the reflection is across the y-axis, the x coordinate will be flipped.

Example: (-7,4) would become (7,4)

6 0

3 years ago

Read 2 more answers

Consider the linear equation y = 2x - 4. Write an equation in slope-

HACTEHA [7]

Answer: y=2x+14

Explanation:
Y=mx+b
Y= 2x-4
M=2

Y= 2x+b

2 = (2 x -6) + b
2=-12+b
12+2=12+b
-12
14=0+b
14=b

Y=2x+14

4 0

3 years ago