For each part, use the Distributive Property to write an equivalent expression
2 answers:
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Answer:
10616 people per square mile
Step-by-step explanation:
No. of people living in the region = 1.2 million
Radius of the area = 6 mile
Since radius of region is given, area of can be calculated by using formula to get area of circle which is where r is radius of circle.
the value of pie is 3.14 which will be used in the calculation
Area of region
population density of any place is calculated by dividing the total population of region with area of the region
mathematically it can be written as
population density of any place = the total population of region / area of the region
substituting the value of total population of region with 1.2 million and area of the region as calculated 113.04 square mile we have
population density of any place = 1.2 million/113.04 square mile
= 0.0106157113 million / square mile
Since one million is equal to 1,000,000
0.0106157113 million will be equal to 0.0106157113 * 1,000,000
= 10615.7113
rounding 10615.7113 nearest to unit value, it will be 10616.
Therefore, population density is 10616 people per square mile.
Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
= x²y cubic feet
1000 = x²y
y = -------(1)
Material used in the prism = Surface area of the rectangular prism
= 2(lb + bh + hl)
Here, h = height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
S = 2(x² + 2xy) - x²
S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² +
= x² +
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x -
2x - = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y =
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.