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.
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<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
Answer:
- Correct choices are selected below
Step-by-step explanation:
- SSS (side, side, side)
- SAS (side, angle, side)
- ASA (angle, side, angle)
- AAS (angle, angle, side)
- HL (hypotenuse, leg)
Answer:
Leah's unit rate is 16 problems per minute.
Step-by-step explanation:
To find her unit rate, we need to find how many problems she can do in 1 minute. Our current fraction is . We need to divide the top and bottom by 2.5 to get the rate per minute
=
Leah's unit rate is 16 problems per minute.
Answer:
A stands for apple
Step-by-step explanation:
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Let, x = The cost of an apple
y = The cost of a peach
6x + 9y = 7.86 - - - - - - - - 1
4x + 5y = 4.82 - - - - - - - - 2
From equation 2,
4x =4.82 - 5y
x= (4.82 - 5y) ÷ 4 - - - - - - - 3
Substitute 3 into 1,
6x + 9y = 7.86
6 [(4.82 - 5y) ÷ 4] + 9y = 7.86
(28.92 - 30 y) ÷4 + 9y = 7.86
28.92 - 30y + 36y = 31.44
6y=2.52
y= 0.42
Substitute y = 0.42 into 2
4x + 5y= 4.82
4x + 5 (0.42) = 4.82
4x + 2.1 = 4.82
4x= 2.72
x= 0.68.
Thus, an apple costs $ 0.68 and a peach costs $ 0.42.