Answer:
none of the above
Step-by-step explanation:
The problem as written cannot have any of the solutions offered.
For any of those choices, the right side expression will be irrational. The left side expression will be rational for any rational value of x, so cannot be equal to the right-side expression.
The solution is an irrational number near ...
x ≈ 1.33682898582
Answer:
The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.
Step-by-step explanation:
The volume (), in cubic centimeters, and surface area (
), in square centimeters, formulas for the candle are described below:
(1)
(2)
Where:
- Radius, in centimeters.
- Height, in centimeters.
By (1) we have an expression of the height in terms of the volume and the radius of the candle:
By substitution in (2) we get the following formula:
Then, we derive the formulas for the First and Second Derivative Tests:
First Derivative Test
There is just one result, since volume is a positive variable.
Second Derivative Test
If :
(which means that the critical value leads to a minimum)
If we know that , then the dimensions for the minimum amount of plastic are:
And the amount of plastic needed to cover the outside of the candle for packaging is:
The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.