Which value is a solution to the inequality 5x – 1 ≤ –11?
2 answers:
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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.
Answer:
The semiannual interest payment is $485.5
The total interest earned over the life of the bond is $10,681
Step-by-step explanation:
The formula of the simple interest is I = Prt, where
- P is the money invested
- r is the interest rate in decimal
- t is the time in years
∵ The bond is $20,000
∴ P = 20,000
∵ First Income Fund 11-year bond at 4.855%
∴ t = 11
∴ r = 4.855%
- Change it to decimal by divide it by 100
∴ r = 4.855 ÷ 100 = 0.04855
∵ The semiannual interest payment = P × r × half a year
∴ The semiannual interest payment = 20,000 × 0.04855 × (1)
∴ The semiannual interest payment = 485.5
The semiannual interest payment is $485.5
∵ I = Prt
- Substitute the values of P, r and t in the formula
∴ I = 20,000(0.04855)(11)
∴ I = 10,681
The total interest earned over the life of the bond is $10,681