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vitfil [10]
3 years ago
10

Gold-192 is a radioactive isotope with a half-life of 4.95 hours. How long will it take for a 15 gram sample of Gold-192 to deca

y until only 3 grams remain?
a. about 11.5 hours

b. about 24.75 hours

c. about 7.92 hours

d. about 2.13 hours
Mathematics
1 answer:
aksik [14]3 years ago
5 0

The answer should be A. In order to solve these half-life problems, I encourage you to find an algebra calculator online, and plug in these numbers. The remaining grams goes in front, so 3.


The entire equation should look something like 3 = 15(1/2)^t/4.95


The 4.95 represents how long it takes before the sample halves, t is your answer, 1/2 represents the value halving every 4.95 hours, 15 is the initial sample size, and 3 is the end result that remains.


The overall answer should be about 11.5 hours, as per an algebra calculator.

Hope this helps solve any other similar problems

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Option B:

Law of cosine, two sides and the included angle are known.

Solution:

Let us first know the law of cosines and law of sines.

Law of cosine:

If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.

c^2=a^2+b^2-2abcos\theta

Law of sine:

The sides of a triangle are to one another  in the same ratio as the sines of their opposite angles.

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

Given ∠P and the sides r, q are known.

<u>To find the value of p:</u>

Option A: Law of cosines, all sides are known.

It is false by the above definition of law of cosine.

Option B: Law of cosine, two sides and the included angle are known.

It is true by the above definition of law of cosine.

Option C: Law of sines, all sides are known.

It is false, because one angle is given in question.

Option D: Law of sines, two angles and the included side are known.

It is false, because two angles are not given.

Option B is the correct answer.

Hence the answer is "Law of cosine, two sides and the included angle are known".

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Step-by-step explanation:

the angle measures of a triangle will always add up to 180

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42+20=62

180-62=118

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