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The mass of cesium left afer 120 years if the original mass of cesium is 8640 with an half-life of 30 years, is 540 grams.
<h3>What is half-life?</h3>This can be defined as the time taken for half the amount of a radioactive substance to decay.
To calculate the amount of cesium left after 120 years, we use the formua below.
Formula:
- R' = R/(
)............. Equation 1
Where:
- R = Original amount of Cesium
- R' = New amount of cesium
- T = Total time
- t = Half-life
From the question,
Given:
- R = 8640
- T = 120 years
- t = 30 years
Substitute these values into equation 1
- R' = 8640/(
)
- R' = 8640/
- R' = 8640/16
- R' = 540 grams.
Hence, The mass of cesium left afer 120 years is 540 grams.
Learn more about half-life here: brainly.com/question/25750315
So for each unit they get $100, so if they sell "x" units, they intake 100x, that's just the gross income, and therefore the Revenue.
Now, they have a cost of 20x + 0.25x² if they "x" units, now, bearing in mind that if you pluck out the costs out of the incoming revenue, what's leftover, is a surplus amount, namely the Profit. Therefore, profit p(x) = revenue - costs, or 100x - (20x + 0.25x²), which is p(x) = -0.25x² +80x.
a)
now, what's the highest profit they can make? check the picture below.
b)
well, if a tax is imposed on them, and say, they take it out of the revenue, then their new revenue is not 100x, is 90x, thus
and you can use the same formula as above to get the x-coordinate for that vertex.
Now, they have a cost of 20x + 0.25x² if they "x" units, now, bearing in mind that if you pluck out the costs out of the incoming revenue, what's leftover, is a surplus amount, namely the Profit. Therefore, profit p(x) = revenue - costs, or 100x - (20x + 0.25x²), which is p(x) = -0.25x² +80x.
a)
now, what's the highest profit they can make? check the picture below.
b)
well, if a tax is imposed on them, and say, they take it out of the revenue, then their new revenue is not 100x, is 90x, thus
and you can use the same formula as above to get the x-coordinate for that vertex.
Step-by-step explanation:
<h2>This problem bothers on the mensuration of flat shapes, composite rectangle. </h2>The correct method for finding the area of a composite rectangle with a large rectangle and a small rectangle connected on the right side are highlighted below.
also see attached the rough sketch of the two rectangles.
- Decompose the figure into two rectangles and add the areas
- Extend the top and rightmost sides to make a larger rectangle, find its area, and then subtract the area of the removed corner.
- Decompose the figure into two rectangles, find their sum, and then subtract the area of the removed corner.
