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Goshia [24]
3 years ago
11

Find dWrite your answer in simplest radical form ​

Mathematics
1 answer:
VladimirAG [237]3 years ago
8 0
It’s so small I couldn’t find the d
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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

#LearnwithBrainly

5 0
2 years ago
Pls help!!!! <br>Evaluate the permutations <br><br><br>1. 6P2<br><br>2. 7P4<br><br>3. 8P3<br><br>​
Gnom [1K]

Answer:

5p9

Step-by-step explanation:

4 0
3 years ago
The height of males approximates a normal distribution. The average height of the players on an NBA team is 6.6 feet with a stan
lara [203]
D) 4.5 Standard Deviations Above the Mean

All you have to do is add .2 to 6.6 until you reach 7.5

6.8
7.0
7.2
7.4

 Then you only need half of .2 to reach 7.5, so it's 4.5 standard deviations above the mean
6 0
3 years ago
What is the value of the expression 0.52?
polet [3.4K]

Answer:

0.25

Step-by-step explanation:

lets say you have half a cake

multiplying a decimal is the same as multiplying its counterpart

basically, you divide half a cake in half

0.25 of a cake, or 1/4

uwu

6 0
2 years ago
Read 2 more answers
-2/3 - (-1 1/3)<br><br> A -1 2/3<br><br> B -2/3<br><br> C-1/3<br><br> D 2/3
mihalych1998 [28]
The answer to your question is D , it is 2/3 simple math even easier if you use a calcul
5 0
3 years ago
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