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8_murik_8 [283]
2 years ago
5

Dylan's Dog weighs 12 times as much as his pet Rabbit. The Dog and Rabbit weigh 104 pounds altogether. How Much does Dylan's Dog

Weigh?
Mathematics
1 answer:
aleksley [76]2 years ago
6 0
When r is the weight of the rabbit:
13r = 104
/13   /13
r = 8
Now, subtract:
104
<span>-   8
</span>= <span>96
</span>Dylan's dog weighs 96 pounds.
Hope this helps!
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Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li
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Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

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Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

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