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finlep [7]
3 years ago
8

Solve by factoring, list steps pleasex^2+8x-20=0

Geography
1 answer:
brilliants [131]3 years ago
7 0
<span>x^2+8x-20=0

Factor the left side of the equation
</span><span><span>(x−2)</span><span>(x+10)</span></span>=<span>0
</span>
Set the factors to both equal the number 0
<span><span>x−2</span>=<span><span><span>0
and/or
</span>x</span>+10</span></span>=<span>0
</span>x = 2 and/or x = -10
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Answer:

The current amount of the Potassium-40 sample is approximately 37.521 grams.

Explanation:

The amount of the sample of the radioactive isotope decays exponentially in time, the amount of mass of the sample as a function of time (m (t)), in grams, is described below:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} } (1)

Where:

m_{o} - Initial mass, in grams.

t - Time, in years.

\tau - Time constant, in years.

The time constant can be found from half life (t_{1/2}), in years, described in statement:

\tau = \frac{t_{1/2}}{\ln 2} (2)

If we know that m_{o} = 300\,g, t = 3.9\times 10^{9}\,yr and t_{1/2} = 1.3\times 10^{9}\,yr, then the current amount of the sample is:

\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}

\tau \approx 1.876\times 10^{9}\,yr

m = (300\,g)\cdot e^{-\frac{3.9\times 10^{9}\,yr}{1.876\times 10^{9}\,yr} }

m\approx  37.521\,g

The current amount of the Potassium-40 sample is approximately 37.521 grams.

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