NetherisIsTheQueen
06.05.2020 •
Mathematics
A rectangular building with a square front is to be constructed of materials that costs 13 dollars per ft2 for the flat roof, 12 dollars per ft2 for the sides and the back, and 17 dollars per ft2 for the glass front. We will ignore the bottom of the building. If the volume of the building is 5,600 ft3, what dimensions will minimize the cost of materials?
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Ответ:
The front side is 11.483 ft while the width of the building is 42.473 ft
Step-by-step explanation:
Volume of the building = 5600 ft³
Area × Width
Side² × Width
Roof dimension = Side × Width
Dimension of side = Side × Width
Dimension of front = Side × Side
Therefore we have, the cost given as follows;
Let the side = S and the width = W
Cost therefore = 13(W·S) +12(2W·S + S²) + 17(S²)
Cost therefore =29·S²+37·W·S
Therefore, we are to minimize 29·S²+37·W·S subject to W·S² = 5600
Which gives
58·S + 37·W = λₓ
37·S = λ
58·S + 37·W = 37·S
37·W = - 21·S
S = -37/21·W
W·S² = 5600
= W·(-37/21·W)² = 5600
W³ = 1803.94
W = 42.473 ft
S = √(5600/42.473)
S = 11.483 ft.
Ответ:
The answer is 12 meters
Step-by-step explanation:
The question asks for the time the ball was thrown, so x = 0, also known as the y intercept, when x is 0, y or in this case the height is 12 meters. The ball was at a height of 12 meters when it was thrown.