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3 years ago

The half-life of a radioactive kind of

Mathematics

2 answers:

Savatey [412]3 years ago

8 0

Answer:

Every 30 years you'll have half left

After 30 years = 900 grams

after 60 years 450 grams

Step-by-step explanation:

Bad White [126]3 years ago

8 0

Answer:

450 gm...this is because we start with 1800/2 = 900 = 30 and 900/2 =450 = 60 yrs. = 450 gm

Step-by-step explanation:

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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

The circumference of a circle is 8cm. What is the diameter of a circle?

USPshnik [31]

Answer:

Hope this helped.

A brainliest is always appreciated.

8 0

2 years ago

Read 2 more answers

What is the solution to this inequality?<br> -4X > 500

Tcecarenko [31]

Answer: x < -125

Step-by-step explanation:

-4x / (-4) < 500 / (-4)

x < -125

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3 years ago

BRAINLIEST!PLEASE HELP ME

kkurt [141]

-12x - 0.4 > 0.2(36.5x + 80) - 55 Remove the brackets.

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- 0.4 > 7.3x + 12x - 39

- 0.4 > 19.3x - 39 Add 39 to both sides.

-0.4 + 39 > 19.3x Combine like terms on the left

38.6 > 19.3x Divide by 19.3

38.6 / 19.3 > x

2 > x

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3 years ago

Solve system by graphing 2x-6y=12 x+y=2

astraxan [27]

First get y by its self , then graph , find intersection point and plug in x and y to both equations, see if it makes sense , then the solution must be you intersection point

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3 years ago