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2 years ago

Find x in the following figure. (Not to scale). Give reasons

Mathematics

1 answer:

Kruka [31]2 years ago

7 0

Answer: 140°, 50°

<u>Step-by-step explanation:</u>

Left picture:

There are 4 sides so the sum of the angles will be 360°. Three angles are given: 90°, 60°, and 70° (their total is 220°). The fourth angle (x) is 360° - 220° = 140°

Right Picture:

There are 5 sides so the sum of the angles will be 540°. Two of the angles are given: 90° and 90°. Two of the angles form a linear pair. Their supplementary angles are: 60° and 70°, so those angles are 120° and 110°

Now, you have four of the five angles: 90°, 90°, 120°, and 110° (their total is 410). The fifth angle (linear pair of x) is 540° - 410° = 130°

The fifth angle is a supplement to x: 180° - 130° = 50°

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What is the value of 5 in the number 583.2

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Step-by-step explanation:

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2 years ago

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.

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

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

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

$e^{-5750k} = 0.5$

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

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$k = 0.00012054733$

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

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

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

$e^{-0.00012054733t} = 0.222$

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

$-0.00012054733t = \ln{0.222}$

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

$t = 12485$

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