Answer:
a. 
b. 
Step-by-step explanation:
First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

The rate is negative as it represents the amount of caffeine leaving the body at certain time.
Answer:
I think it is commutative
Step-by-step explanation:
because commute means move so I think that's what it is
Answer:
3 n minus 4 represents the expression "four less than three times a number"
Answer:
Part One: $187
Part Two: 11a + 5.5k
Step-by-step explanation:
Part One:
a = 9 (how many adult tickets)
k = 16 (how many kid tickets)
($11 × a) + ($5.50 × k) = total cost
($11 × 9) + ($5.50 × 16)
($99) + ($88) = $187 = total cost
Part Two:
11a + 5.5k
11 is how much the adult ticket costs, you multiply a or the amount of adult tickets in order to get the total cost for adults.
5.5 is how much the kid ticket costs, you multiply k or the amount of kid tickets in order to get the total cost for kids.
you add 11a + 5.5k or the total cost for adults and the total cost for kids to get the total cost.
Answer:
Step-by-step explanation:
Integer roots:
a = 6 n + 1, b = 7, c = -3 n^2 - n, n element Z
a = 6 n + 5, b = 7, c = -3 n^2 - 5 n - 2, n element Z
Derivative:
d/da(1/7 (a^2 + 12 c) b - 1) = (2 a b)/7
Indefinite integral:
integral(-1 + 1/7 b (a^2 + 12 c)) da = (a^3 b)/21 + (12 a b c)/7 - a + constant
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