Waht is the first six nonzero multiples
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
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Answer:
The fraction of total interest owed is
The value of it to the nearest tenth is 73.1%
Step-by-step explanation:
Let us solve it using the rule of 78
∵ The loan = 12 month
∵ The numerator is after 6 month
- Substitute n by 1 in each bracket
∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}
∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}
∴ The numerator = {57}
∴ The numerator of the fraction is 57
∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}
- substitute n by 1 in each bracket
∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}
∴ The denominator = {78}
∴ The denominator of the fraction is 78
The fraction of total interest owed is
Now find the value of the fraction
∵ The fraction =
∴ Its value = 0.7307692308 × 100%
∴ Its value = 73.07692308%
- Round it to the nearest tenth
∴ Its value = 73.1%
The value of it to the nearest tenth is 73.1%