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fgiga [73]
3 years ago
5

A radioactive substance has a continuous decay rate of 0.056 per minute. How many grams of a 120 gram sample will remain radioac

tive after 40 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.
Mathematics
1 answer:
sammy [17]3 years ago
5 0

Answer:

The mass of the radioactive sample after 40 minutes is 12.8 g.

Step-by-step explanation:

The mass of the sample can be found by using the exponential decay equation:

N_{t} = N_{0}e^{-\lambda t}

Where:

N(t): is the amount of the sample at time t =?

N₀: is the initial quantity of the sample = 120 g

t = 40 min

λ: is the decay constant =  0.056 min⁻¹

Hence, the mass of the sample after 40 min is:

N_{t} = N_{0}e^{-\lambda t} = 120g*e^{-0.056min^{-1}*40 min} = 12.8 g

     

Therefore, the mass of the radioactive sample after 40 minutes is 12.8 g.

I hope it helps you!

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Find the number that makes the ratio equivalent to 1:2.<br> 9:
Y_Kistochka [10]

Answer:

9:18

Step-by-step explanation:

1:2 means that you have to multiply the first number by 2 to get the second number. Therefore, you have to multiply 9 by 2, which is equal to 18. Therefore, it would be 9:18.

If this has helped please mark as brainliest

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3 years ago
Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is i
Romashka-Z-Leto [24]

0.08 cm/min

Step-by-step explanation:

Given:

\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}

Find \frac{dr}{dt} when diameter D = 20 cm.

We know that the volume of a sphere is given by

V = \dfrac{4\pi}{3}r^3

Taking the time derivative of V, we get

\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}

Solving for \frac{dr}{dt}, we get

\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})

\:\:\:\:\:\:\:= 0.08\:\text{cm/min}

3 0
3 years ago
What is 4/10 of 0.04
cluponka [151]
4/10  x 0.04 = (of means multiply)
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0.016
3 0
3 years ago
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Suppose that a rectangular picture is surrounded by a frame of uniform width of x
user100 [1]

Answer:

Ok so the area of the frame is 18*12 = 216cm^2

Let’s suppose the width of the frame is x

The total area (painting and frame) is (2x+18)(2x+12) and this is equal to 432

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4x^2 + 60x - 216 = 0

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3 years ago
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serious [3.7K]

Answer:

A: -6.5

Step-by-step explanation:

Take two points that we already know are on the line and find the slope

I used:

(4, -10) and (7, -30)

X1 (first x coordinate): 4

Y1 (first y coordinate): -10

X2 (second x coordinate): 7

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The closest answer to that is A.

3 0
3 years ago
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