Solve the problem. Find the amount of money in an account after 12 years if $4700 is deposited at 5% annual interest compounded
1 answer:
Answer:
The correct answer is $8532.17
Step-by-step explanation:
The formula for calculating investments with compound interests is as follows:
Where:
R is the annual interest rate,
t is the number of times the investment is to be compounded in a year,
n is the number of years,
P is the principal amount invested.
Replacing in the formula with the given values you have:
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Answer:
The square-based box with the greatest volume under the condition that the sum of length, width, and heigth does not exceed 174 in is a cube with each edge of 58 in and a volume of
Step-by-step explanation:
For this problem we have two constraints, that are as follows:
1) Sum of length, width, and heigth not exceeding 174 in
2) Lenght and width have the same measure (square-based box)
We know that volume is equal to the product of all three edges, and with the two conditions into account we have the next function:
The interval of interest of the objective function is [0, 87]
This problem requieres that we maximize the function that defines the volume. We start calculating the derivative of the function, wich is:
We need to remember that the derivative of a function represents the slope of said function at a given point. The maximum value of the function will have a slope equal to zero.
So we find the value in wich the derivative equals zero:
The first value () will leave us with a 'height-only box', so the answer must be
The value is between the interval of interest.
And, once we solve for the constraints, we have that:
Lenght = Width = Heigth = 58 in
Volume =