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2 answers:
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Answer:
A
Step-by-step explanation:
In a right triangle, the side opposite to the 90 degree angle (here, side opposite to angle A) is known as the hypotenuse.
Also, the side that is "opposite" to the angle given (here side opposite is y to angle given 30 degrees) is the opposite side.
Since we want to find "opposite" and have "hypotenuse" , recalling trig ratios, we can say opposite/hypotenuse is the ratio SINE, so we can write:
We solve for y:
Since the answer choice has angles in radians, we recall 30 degrees is radians.
Thus, the correct answer is , or option A
Answer:
<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.
An exponential decay can be described by the following formula:
Where:
No = The quantity of the substance that will decay.
N(t) = The quantity that still remains and has not yet decayed after a time t
= The decay constant.
One important parameter related to radioactive decay is the half-life:
If we know the value of the half-life, we can calculate the decay constant:
Carbon-14 has a half-life of 5,730 years, thus:
The equation of the remaining quantity of Carbon-14 is:
We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No
Simplifying:
Taking logarithms:
Solving for t:
Carbon-14 will take 19,035 years to decay to 10 percent.