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.
For P(t) = 920*1.06^(2t), the current population is 920, the percentage growth rate is 6% semiannually, and the population in 4 years will be 920*1.06^8 = 1466.
Selection B is appropriate.
_____
The 2 in the exponent means the growth factor 1.06 is applied twice for each increment of t, that is, twice in 1 year (semiannually).
Answer:
x = 5
Step-by-step explanation:
Hello!
For this equation, we start by combining like terms. Since we have two terms with the same variable, we are able to add them together:
3x + 2x + 7 = 32
5x + 7 = 32
As you can see, we added 3x and 2x together.
Now, since we are aiming to get x by itself, we need to subtract 7, from both sides:
5x + 7 = 32
5x = 25
Finally, we divide the 5 attached onto the x by itself, which will leave the x alone on one side:
5x = 25
x = 5
Again, we divided on both sides.
And, there you have it!
x = 5
Hope I helped!
-Mary
please give brainliest
C(T) = 26(0.87)^(T)
open the pdf, it gives the answer
you're welcome! ^-^