Answer:
The signed number that indicates how much of the levee will erode during the next decade is:
-30 feet
Step-by-step explanation:
a) Data and Calculations:
Erosion rate of the banks of the levee = 3 feet per year
For 10 years, if nothing is done to correct the problem, the eroded banks will be equal to 10 * 3 = 30 feet
Therefore, the signed erosion in the next decade is -30 feet.
b) The quantity of erosion can be given as the number of years involved without correction, multiplied by the rate of erosion per year. This implies that the quantity of erosion depends on the number of years and the rate of erosion per year.
If the growth rate is a constant, we can model it using a linear equation:
y = b + ax
where b = initial value, a = growth rate.
In this case, x = m = number of months.
Let's find the equation for the growth of each species.
Species A:
Initial height = b = 25 cm
Growth rate = a = 3 cm per month
So its height can be modeled by H(m) = 25 + 3m
Species B:
Initial height = b = 10 cm
Growth rate = a = 8 cm per month
So its height can be modeled by H(m) = 10 + 8m
Thus the answer is A: H(m) = 25 + 3m and B: H(m) = 10 + 8m.
The solution is 1/4 because 25/100 / 25/25 1/4
Answer:
Each pitcher has the same fraction of the other drink.
Step-by-step explanation:
After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).
The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.
_____
You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.
Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:
tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2
d - 3 = (-8)
+3 +3
d = -5
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