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xxMikexx [17]
2 years ago
11

Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample

of Element X is 100 grams, how long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?
Mathematics
1 answer:
Lena [83]2 years ago
8 0

Answer:

19.3 years

Step-by-step explanation:

Given that the initial mass of a sample of Element X is 100 grams,

The formula is given as:

N(t) = No × (1/2) ^t/t½

Element X is a radioactive isotope such that every 30 years, its mass decreases by half.

N(t) = Mass after time (t)

No = Initial mass = 100 grams

t½ = Half life = 30 grams

N(t) = 100 × (1/2) ^t/30

How long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?

This means we are to find the time

N(t) = 100 × (1/2) ^t/30

N(t) = 64 grams

64 = 100(1/2)^t/30

Divide both sides by 100

64/100 = 100(1/2)^t/30/100

0.64 = (1/2)^t/30

Take the Log of both sides

log 0.64 = log (1/2)^t/30

log 0.64 = t/30(1/2)

t = 19.315685693242 years

Approximately = 19.3 years

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Step-by-step explanation:

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Y is directly related to X, and Y is 81 when X is 27.<br> The constant of variation is ____
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Answer:x=3/9

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{ PLEASE ANSWER QUICKLY, PROBLEM DUE ASAP } The functions f(x) and g(x) are defined below. Which expression is equal to f(x) + g
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7 0
3 years ago
Travis jogged to his friend's house 10 miles away and then got a ride back home. It took him 2 hours longer to jog there than ri
spin [16.1K]

Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.

<h3>What is the relation between velocity, distance and time?</h3>

Velocity is <u>distance divided by time,</u> hence:

v = \frac{d}{t}

Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:

v = \frac{10}{t + 2}

Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:

v + 16 = \frac{10}{t}

Then, considering the first equation and replacing in the second:

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\frac{10}{t} - \frac{10}{t + 2} = 16

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16t² + 32t - 20 = 0 -> t = 0.5.

Then his jogging rate in mph was:

v = \frac{10}{0.5 + 2} = 4.5

More can be learned about the relation between velocity, distance and time at brainly.com/question/24316569

#SPJ1

8 0
2 years ago
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