List the first 9 terms of the sequence defined recursively by Sn = Sn-2. (Sn-1 - 1), with S1 = 2 and
1 answer:
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Answer:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Step-by-step explanation:
This is a optimization with restrictions problem.
The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).
This restriction can be expressed as:
being x: the side of the square of the cross section and L: length of the package.
The volume, that we want to maximize, is:
If we express L in function of x using the restriction equation, we get:
We replace L in the volume formula and we get
To maximize the volume we derive and equal to 0
We can replace x to calculate L:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Interest paid after 30 years is $494,546.99.
Solution:
Principal (P) = $195,000
Interest rate (r) = 4.3%
Time (t) = 30 years
n = number of times interest calculated per year
n = 1
Compound interest formula:
where A is the final amount
A = 689546.99
Interest = Amount - Principal
= 689546.99 - 195000
= 494546.99
Interest paid after 30 years is $494,546.99.
Answer:
x<56
Step-by-step explanation:
Since the dot over 56 isn't filled in, the inequality doesn't include 56 (so we'll use < or > not or
)
Now, let's look at the direction of the shading: is it going to the left of 56 or to the right?
This shading is to the left of 56, which indicates that it's all of the numbers less than 56.
As said above, the inequality doesn't include 56
therefore, it will be x<56 (x is less than 56, and 56 is not included)
hope this helps!