Answer:
- front/back: 106 2/3 ft
- sides: 135 ft
Step-by-step explanation:
These problems are easily solved if you start with the knowledge that the solution makes the front/back cost equal to the side cost.
Suppose we define the length of the front as x. Then the total cost of the front and back is (2x)(81) = 162x.
If y is the length of the side of the building, then (2y)(64) = 128y is the total cost of the sides of the building. When these costs are equal, we have ...
162x = 128y
y = (162/128)x
The floor area is ...
xy = 14400 = x(162/128)x
x = √(14400·128/162) = √(11377 7/9) = 106 2/3
y = (162/128)x = 135
The front/back of the building measure 106 ft 8 inches; the sides measure 135 feet.
_____
<em>Solution using derivatives</em>
Using the above variable definitions, we can find the side length as ...
y = 14400/x
so the total cost is then ...
c = 162x + 128(14400/x)
We want the derivative with respect to x to be zero:
dc/dx = 0 = 162 -128·14400/x^2
Solving for x gives ...
x = √(14400·128/162) = 106 2/3 . . . . . compare to the solution above
y = 14400/(106 2/3) = 135
X + 3x + 4x = 56
8x = 56
x = 7
The shortest piece is 7 inches
The middle piece is 7*3 = 21 inches.
The longest piece is 4*7 = 28 inches
Check
7 + 21 + 28 = 56 It does check and the lengths are correct.
Answer:
for 48, the prime numbers I have obtained are 2, 3, 2, 2, and 2
That is not a question. Did you mean $270 to pesos? Or 3000 pesos to Us
Answer:
It should be in between 8 or 9