Answer:
The bones were 12,485 years old at the time they were discovered.
Step-by-step explanation:
Amount of the element:
The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

In which A(0) is the initial amount and k is the decay rate, as a decimal.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that
, and we use this to find k. So







So

A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Had 100 - 77.8 = 22.2% remaining, so this is t for which:

Then






The bones were 12,485 years old at the time they were discovered.
Answer:
The radius of a sphere hides inside its absolute roundness. A sphere's radius is the length from the sphere's center to any point on its surface. The radius is an identifying trait, and from it other measurements of the sphere can be calculated, including its circumference, surface area and volume. The formula to determine the volume of a sphere is 4/3π multiplied by r, the radius, cubed, where π, or pi, is a non terminating and non repeating mathematical constant commonly rounded off to 3.1416. Since we know the volume, we can plug in the other numbers to solve for the radius, r.
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Multiply the volume by 3. For example, suppose the volume of the sphere is 100 cubic units. Multiplying that amount by 3 equals 300.
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Divide this figure by 4π. In this example, dividing 300 by 4π gives a quotient of 23.873.
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Calculate the cube root of that number. For this example, the cube root of 23.873 equals 2.879. The radius is 2.879 units.
Answer:
|x-22| < 2
The < has an underline below it
A scientific theory is a validated explanation of some aspect of the natural world, based on multiple facts that have been frequently verified through research and experimentation. Fact theories are not "guesses" but reliable accounts of the real world.
Answer:
-4sinθcosθ
Step-by-step explanation:
Note:
1. (a + b)^2 = a^2 + 2ab + b^2
2. (a - b)^2 = a^2 - 2ab + b^2
3. sin^2θ + cos^2θ = 1
(sinθ -cosθ)^2 - (sinθ + cosθ)^2
= sin^2θ - 2sinθcosθ + cos^2θ - (sin^2θ + 2sinθcosθ + cos^2θ)
= sin^2θ + cos^2θ - 2sinθcosθ - (sin^2θ + cos^2θ + 2sinθcosθ)
= 1 - 2sinθcosθ - (1 + 2sinθcosθ)
= 1- 2sinθcosθ -1 - 2sinθcosθ
= - 2sinθcosθ - 2sinθcosθ
= -4sinθcosθ