PLS HELP ASAP (THE PICTURE IS BELLOW)
2 answers:
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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.
Answer:
The population of California is more than the population of Wyoming.
Alternatively, the population of California is times the population of Wyoming.
Step-by-step explanation:
The first part is to take the numbers out of the scientific notation. The estimated population of California is 38,800,000, and the population of Wyoming is 584,000.
Not that we've done that, let's start with the first part of the problem.
"The population of California is __________ more than the population of Wyoming."
This is a statement of subtraction, because it's not asking how many TIMES more. So, we subtract Wyoming's population from California's population.
Putting that number into scientific notation is easy: move the decimal to the place in the number where there will only be one number in front of the decimal: 3.3216. How many number slots until you have only one number in front of the decimal? 7. So, we know that the power of 10 is going to be 7. So, the first part of the question answers to:
Now for the second part.
"Alternatively, the population of California is _________ times the population of Wyoming."
This is a problem of division. The question is asking us to divide California's population by Wyoming's population.
We need to have one number in front of the decimal point, so we move it behind the first 6, giving us 6.64. Because we did this, we need to bump the exponent from 2 to 1, leaving us with:
So, the answer to the question is:
1.
2.
Hope this helped you, and I hope you get a perfect score!! :)