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2 years ago

Evaluate √16-x when x=8.

Mathematics

1 answer:

PIT_PIT [208]2 years ago

3 0

D
Sq rt of 8 is sq rt of 4 times sq rt of 2

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he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

elena-s [515]

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:

$A(t) = A(0)e^{-kt}$

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 $A(5750) = 0.5A(0)$ , and we use this to find k. So

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-5750k}$

$e^{-5750k} = 0.5$

$\ln{e^{-5750k}} = \ln{0.5}$

$-5750k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{5750}$

$k = 0.00012054733$

$A(t) = A(0)e^{-0.00012054733t}$

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:

$A(t) = 0.222A(0)$

Then

$0.222A(0) = A(0)e^{-0.00012054733t}$

$e^{-0.00012054733t} = 0.222$

$\ln{e^{-0.00012054733t}} = \ln{0.222}$

$-0.00012054733t = \ln{0.222}$

$t = -\frac{\ln{0.222}}{0.00012054733}$

$t = 12485$

The bones were 12,485 years old at the time they were discovered.

8 0

2 years ago

Two parallel lines are crossed by a transversal what is the value of A?

gulaghasi [49]

Answer: 63 degrees (second choice)

The two angles shown are corresponding angles. They are both on the bottom side of their adjacent parallel line, and at the same time, they are also on the left side of the transversal line. This is why they are corresponding angles.

Corresponding angles are congruent if you have a set of parallel lines like the diagram shows. So that's why a = 63.

3 0

2 years ago

From 1995-2005, the hourly pay for lifeguards at an outdoor swimming pool increased by 2% per year. The hourly pay, P(t), in dol

12345 [234]

Answer:

The hourly pay for the lifeguards in 2001 was of $6.31.

Step-by-step explanation:

The hourly pay, in dollars, in t years after 1995, is given by the following equation:

$P(t) = 5.60(1.02)^{t}$