Answer:
250 minutes with the flat rate of $29.
x would be the number of minutes called.
Tracy would be charged by $0.35 per minute.
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Answer:
First number: -39
Second number: -37
Step-by-step explanation:
An odd number can be written as where n is a whole number.
Let's call our first number 2n+1.
Our second, consecutive number will be 2 more than our first number, since it has to be odd. All numbers go: odd -> even -> odd -> even. If we have an odd number, and add 2, we'll get the next odd number.
First number: 2n+1
Second number: 2n+1+2 = 2n+3
The sum of these two numbers, 2n+1 and 2n+3 will be -76.
(2n+1) + (2n+3) = -76
2n + 2n + 1 + 3 = -76
4n + 4 = -76
4n = -80
n = -20
Since our first number is 2n+1:
2 * (-20) + 1 = -40 + 1 = -39
First number: -39
Our second number is 2n+3, or 2 more than our first number.
-39 + 2 = -37
Second number: -37
We can double check this:
-39 + (-37) = -39 - 37 = -76
Answer:
The largest possible volume of the box is 2000000 cubic meters.
Step-by-step explanation:
The volume (), in cubic centimeters, and surface area (
), in square centimeters, of the box with a square base are described below:
(1)
(2)
Where:
- Side length of the base, in centimeters.
- Height of the box, in centimeters.
By (2), we clear within the formula:
And we apply in (1) and simplify the resulting expression:
(3)
Then, we find the first and second derivatives of this expression:
(4)
(5)
If and
, then we find the critical value of the side length of the base is:
Then, we evaluate this result in the expression of the second derivative:
By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:
The largest possible volume of the box is 2000000 cubic meters.