Find the area! Please help me
1 answer:
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Illustrate the given problem. Refer to the diagram attached to aid our solution.
Area of bigger rectangle:
A = (L+8)(W+16)
Area of smaller rectangle (printed area)
388 = LW
From the second equation, we can express L in terms of W.
L = 388/W
Replace this to the first equation:
A = (388/W+8)(W+16)
A = 388 + 6208/W + 8W + 128
A = 6208/W + 8W + 516
Derive A with respect to W and equate to zero (calculus):
dA/dW = -6208/W² + 8 = 0
-6208/W² = -8
W² = -6208/-8 = 776
W = √776 = 27.86 cm
L = 388/27.86 = 13.93 cm
Thus, the smallest area would be:
A = (13.93 cm)(27.86 cm)
<em>A = 388.09 cm²</em>
Area of bigger rectangle:
A = (L+8)(W+16)
Area of smaller rectangle (printed area)
388 = LW
From the second equation, we can express L in terms of W.
L = 388/W
Replace this to the first equation:
A = (388/W+8)(W+16)
A = 388 + 6208/W + 8W + 128
A = 6208/W + 8W + 516
Derive A with respect to W and equate to zero (calculus):
dA/dW = -6208/W² + 8 = 0
-6208/W² = -8
W² = -6208/-8 = 776
W = √776 = 27.86 cm
L = 388/27.86 = 13.93 cm
Thus, the smallest area would be:
A = (13.93 cm)(27.86 cm)
<em>A = 388.09 cm²</em>
Using the interest formulas, it is found that the values of the investment are given as follows:
- Using simple interest, the value will be of $34,000.
- Using compound interest, the value will be of $144,461.
- Using continuous compounding, the value will be of $148,002.
Simple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
In which:
- P is the initial amount.
- r is the interest rate, as a decimal.
In this problem, we have that the parameters are as follows:
P = 9000, r = 0.07, t = 40.
Hence:
n is the number of compounding, for quarterly n = 4, then:
Hence:
More can be learned about the interest formulas at brainly.com/question/25296782
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