An office supply warehouse has large boxes of folders. Each box has 550 folders. How many folders are there in 23 boxes?

A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing

Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

A fence must be built to enclose a rectangular area of 20,000 ft²
Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ $y=\frac{20,000}{x}$

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

North and South

∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

∴ $C=8x+16(\frac{20,000}{x})$

∴ $C=8x+\frac{320,000}{x}$

To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x

∵ $\frac{320,000}{x}$ can be written as $320,000x^{-1}$

∴ $C=8x+320,000x^{-1}$

∵ $\frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}$

∴ $\frac{dC}{dx}=8-320,000x^{-2}$

- Equate $\frac{dC}{dx}$ by zero

∴ $8-320,000x^{-2}=0$

∵ $-320,000x^{-2}=-\frac{320,000}{x^{2}}$

∴ $8-\frac{320,000}{x^{2}}=0$

- Subtract 8 from both sides

∴ $-\frac{320,000}{x^{2}}=-8$

- Multiply both sides by x²

∴ - 320,000 = - 8x²

- Divide both sides by -8

∴ 40,000 = x²

- Take √ for both sides

∴ 200 = x

Substitute x in the equation of C to find the least cost of fence

∵ $C=8(200)+\frac{320,000}{(200)}$

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

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Find the variable in xy=6b

Mkey [24]

Xy=6b
/y . /y
x=6by
that is the answer because there is no true answer

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How is the graph of the parent function y=x² transformed to produce the graph of y=3(x+1)²?

Anna11 [10]

Answer:

Step-by-step explanation:

Remark

Always the easiest way to study these questions is to get a graph. The one below shows

Red: y = x^2

Blue: y= 3(x + 1)^2

You will notice that (x+1)^2 shifts the graph Left -- the opposite to what you might think.

The 3 is a little harder. It narrows the red mother graph. Which choice says that?

The choice is between b and d. Why. Because the blue graph is to the left of the red one.

You have to learn the meaning of compressed. A better word might be narrows.

Answer

B

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The high temperature one day was -1 F. The low temperature was -5 F. What was the difference between the high and low temperatur

zhuklara [117]

The difference is 4 degrees Fahrenheit

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Justify conclusion on why 2 ounces of ketchup is ok to use when eating potatoe wedges

ikadub [295]

Well you haven't really given us a question that requires a "quantifiable" answer. 2 ounces is roughly equivalent to 60 grams. 2 ounces of ketchup wouldn't be an awful lot of ketchup. I'm sure that you'd remain healthy despite eating 2 ounces of ketchup along with your potato wedges.

According to the American Heart Association, women should only have about 25 grams of sugar per day. In 100g of ketchup there would be about 22g grams of sugar. If you were to eat roughly 60g of ketchup, you'd only be digesting about 13.2 grams of sugar. Now, potato wedges could also contain sugar, but you haven't stated how many grams or kilograms of potato wedges you'd be eating, so I wouldn't be able to tell you whether your meal contains too much sugar.

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