Charity sold 110 cookies for $0.75 each. Her cost to make each cookie was $0.20 plus $20 for boxes. How much profit will charity
1 answer:
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Answer:
24761 mosquitoes
5.4 days
Step-by-step explanation:
Let the equation that shows the population of the mosquitoes after x days,
Where,
P = Initial population,
r = rate of increasing per day,
Here, A = 1000, when x = 0,
A = 1900 when x = 1,
Thus, the required function that represents the population after x days,
If x = 4,
The number of mosquito after 4 days,
If A = 60,000,
Taking log both sides,
Thus, there will 60,000 mosquitoes after 5 days.
Answer:
92
Step-by-step explanation:
Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...
x²(5-x)³
A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.
The difference between the maximum and minimum is 108-16 = 92.
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If you like, you can take the derivative and set it to zero.
f(x) = x²(5 -x)³
f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)
f'(x) = 5x(5-x)²(2-x)
This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.
To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...
f(1) = 1²·4³ = 64
f(2) = 2²·3³ = 108 . . . . product maximum
f(4) = 4²·1³ = 16 . . . . . . product minimum
The difference between the maximum and minimum is 92.
