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2 years ago

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Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample

of Element X is 390 grams, how long would it be until the mass of the sample reached 260 grams, to the nearest tenth of a year?

1 answer:

SSSSS [86.1K]2 years ago

8 0

Answer:

It will take 15.029 years for element X to reach mass of 260 grams

Step-by-step explanation:

The half life period of radioactive element X is 26 years

The initial mass of radioactive element X is 260 grams

Elapsed time = half life * log (beginning amount /ending amount)/log 2

Substituting the given values, we get

Elapsed time = 26 * log (390/260)/log 2

= 15.209 years

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2 years ago

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Answer:

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Step-by-step explanation:

We proceed to derive each expression by rule of chain. Let be $w = \ln (x+2\cdot y + 3\cdot z)$ , $x = r^{2}+t^{2}$ , $y = s^{2}-t^{2}$ and $z = r^{2}+s^{2}$ :

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$\frac{dw}{dr} = \frac{8\cdot r}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}$

$\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ (1)

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$\frac{dx}{ds} = 0$

$\frac{dy}{ds} = 2\cdot s$

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$\frac{dw}{dt} = \frac{\frac{dx}{dt}+2\cdot \frac{dy}{dt} +3\cdot \frac{dz}{dt} }{x+2\cdot y + 3\cdot z}$

$\frac{dx}{dt} = 2\cdot t$

$\frac{dy}{dt} = -2\cdot t$

$\frac{dz}{dt} = 0$

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3 years ago

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Let me help you!

Ok, so before I give you the answer, which is very simple, I will first show you how to answer questions like this in the future.

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To make it clearer:
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*** By the way, when counting the range, we don't start at 1, we start at 0. That's why even if the range is 5, the last value is 4.

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