Multiply and simplify: (6x + 3y)(6x − 3y)
2 answers:
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Answer:
a) The volume of the box is represented by .
b) A side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.
Step-by-step explanation:
a) The volume of the box (), in cubic inches, is modelled by the equation for the cuboid:
(1)
Where is the side length of the cutted square corners, in inches.
The volume of the box is represented by .
b) The method consist in graphing the polynomial and looking for a relative maximum. We graph the equation found in a) by means of a graphic tool. We present the outcome in the image attached below. According to this, a side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.
B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.
Now, notice that
That is, we can write the sum more compactly as
The series is geometric with common ratio
, so the series converges (and thereby has a sum), so the answer is D.
Now, notice that
That is, we can write the sum more compactly as
The series is geometric with common ratio