Using proportions, it is found that the differential equation which describes the growth of the pigeon population is given by:
![\frac{dP}{dt} = 1.5P](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%201.5P)
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, considering the initial population and the population one week later, the rate of growth is given by:
k = 9/6 = 1.5.
The standard differential equation for population growth is:
![\frac{dP}{dt} = kP](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20kP)
Hence:
![\frac{dP}{dt} = 1.5P](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%201.5P)
More can be learned about proportions at brainly.com/question/24372153
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Answer:
111111
1111110 is the simple expression.
Step-by-step explanation:
The expression to be solved:
![\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%2C666%2C666%5Ctimes666%2C666%20%7D%7B1%2B2%2B3%2B4%2B5%2B6%2B5%2B4%2B3%2B2%2B1%7D%20-%20%5Cdfrac%7B777%2C777%5Ctimes777%2C777%7D%7B1%2B2%2B3%2B4%2B5%2B6%2B7%2B6%2B5%2B4%2B3%2B2%2B1%7D)
First of all, let us solve the first term:
![\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111](https://tex.z-dn.net/?f=%5Cdfrac%7B6%2C666%2C666%5Ctimes666%2C666%20%7D%7B1%2B2%2B3%2B4%2B5%2B6%2B5%2B4%2B3%2B2%2B1%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B6666666%5Ctimes666666%20%7D%7B36%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B6666666%5Ctimes666666%20%7D%7B6%5Ctimes%206%7D%5C%5C%5CRightarrow%201111111%5Ctimes%20111111)
Now, the right term:
![\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111](https://tex.z-dn.net/?f=%5Cdfrac%7B777777%5Ctimes777777%7D%7B1%2B2%2B3%2B4%2B5%2B6%2B7%2B6%2B5%2B4%2B3%2B2%2B1%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B777777%5Ctimes777777%7D%7B49%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B777777%5Ctimes777777%7D%7B7%20%5Ctimes%207%7D%5C%5C%5CRightarrow%20111111%20%5Ctimes%20111111)
So, the expression to be solved becomes:
![1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110](https://tex.z-dn.net/?f=1111111%5Ctimes%20111111-111111%5Ctimes%20111111%5C%5C%5CRightarrow%20111111%281111111-1%29%5C%5C%5CRightarrow%20111111%5Ctimes%201111110)
Answer: the final mass of the solid is 176 grams.
Step-by-step explanation:
The "change" between two quantities, one initial Qi and one final Qf is defined as:
Change = Qf - Qi.
In this case, the quantity is mass, and we know that the initial mass is 260 grams.
And we also know that the change is -84 grams.
Then we have the equation:
Qf - 260 g = -84g
Qf = -84g + 260g = 176g
So the final mass of the solid is 176 grams.