A box of 8 crayons costs $0.96. How much does
1 answer:
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Answer:
The highest achievable volume for the box is 2000000 cubic meters.
Step-by-step explanation:
Below is an outline of the volume (), measured in cubic centimeters, and surface area (
), measured in square centimeters, for a box featuring a square base:
(1)
(2)
Where:
- The length of the base's side, in centimeters.
- The height of the box, in centimeters.
Using (2), we isolate in the formula:
Then, we substitute into (1) and simplify the outcome:
(3)
Next, we calculate the first and second derivatives of this expression:
(4)
(5)
If and
, then we find that the critical value for the base's side length is:
Subsequently, we assess this outcome using the second derivative's expression:
According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:
The highest achievable volume for the box is 2000000 cubic meters.
Response:
The factored expression is
.
Detailed explanation:
Provided:
Our goal is to express the given equation in a factored form.
Factoring pertains to rewriting an expression so that the product of its factors yields the original expression
Let’s consider the expression .
We recognize the algebraic identity
Thus, we have .
Matching with the above identity, we assign x= a, and b = 11, leading to
.
Consequently, the factored expression is
.