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Mila [183]
3 years ago
12

The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass

. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Mathematics
1 answer:
TiliK225 [7]3 years ago
7 0

Answer:

3 grams will be left after 6 half-lives

Step-by-step explanation:

Half-live:

Time it takes for the substance to be reduced by hall.

After n half lives:

The amount remaing is:

A(n) = A(0)(0.5)^{n}

In which A(0) is the initial amount and n is the number of half-lives.

Starting with 210 grams of a radioactive isotope, how much will be left after 6 half-lives?

This is A(6) when A(0) = 210. So

A(n) = A(0)(0.5)^{n}

A(6) = 210(0.5)^{6} = 3.3

Rounding to the nearest gram

3 grams will be left after 6 half-lives

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Determine whether the function ƒ(x) = x4(x2 − 1) is even, odd or neither.
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PLEASE HELP ME
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Answer:

  • The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.

Explanation:

By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.

You can check that analitically

Departing from the triangle: XYZ

  • <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)

  • Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
  • Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
  • Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)

  • <u>Translation 1 unit down</u>: (x,y) → (x, y-1)

  • (-11,2) → (-11, 2 - 1) = (-11, 1)
  • (-9,7) → (-9, 7 - 1) = (-9, 6)
  • (-7, 2) → (-7, 2 - 1) = (-7, 1)

  • <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)

  • (-11, 1) → (-11, -1), which are the coordinates of vertex X"
  • (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
  • (-7, 1) → (-7, -1), which are the coordinates of vertex Z"

Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

7 0
2 years ago
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