Answer:
a. length = 0.7211 ft
b. width = 0.7211 ft
c. height = 140.3846 ft
Step-by-step explanation:
This is an optimiztion with restriction problem.
We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.
As the cost for the sides is constant, we know that length and width are equal.
Then, we can express the volume as:
being x: length and z: height
We can express the height in function of the length as:
Then, the cost of the box can be expressed as:
To optimize C, we derive and equal to zero
![\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211](https://tex.z-dn.net/?f=%5Cdfrac%7BdC%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5B0.8x%5E2%2B0.6x%5E%7B-1%7D%5D%3D1.6x-0.6x%5E%7B-2%7D%3D0%5C%5C%5C%5C%5C%5C1.6x%3D0.6x%5E%7B-2%7D%5C%5C%5C%5Cx%5E%7B1%2B2%7D%3D0.6%2F1.6%3D0.375%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B0.375%7D%20%3D0.7211)
The height z is then
Answer:
5/2, 4/5 are terminating decimals
Step-by-step explanation:
5/2 = 2.5 this is a terminating decimal
4/5 = .8 this is a terminating decimal
2/7 = .285714(repeating) This is a repeating decimal
4/3 = 1.3(repeating) this is a repeating decimal
Answer:
5 m/min
Step-by-step explanation:
Initial speed = 6 m/ min
Final speedd = 4 m/ min
Average speed = 
Avg. Speed = 5 m / min.
Answer:
Step-by-step explanation:
p=8 cm
one side=8/4=2 cm
edge of black square=2/4=1/2 cm=0.5 cm
area of one square=(0.5)²=0.25 cm²
total area of two black squares=2×0.25=0.5 cm²
length of white rectangle=2/2=1 cm
width=2/4=1/2 cm=0.5 cm
area of one rectangle=1×0.5=0.5 cm²
area of two rectangles=2×0.5=1 cm²
total area=0.5+1=1.5 cm ²
