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AveGali [126]
3 years ago
6

What is f(x)=x; g(x)=x+3

Mathematics
1 answer:
eduard3 years ago
3 0

Answer:

A

Step-by-step explanation:


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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
3 years ago
What is the value of <img src="https://tex.z-dn.net/?f=%20a_%7B1%7D%20" id="TexFormula1" title=" a_{1} " alt=" a_{1} " align="ab
julia-pushkina [17]
The correct awnser is a or c i hope i helped
8 0
3 years ago
Eya is 5 years younger than 3 times Bills age. If Eya is 28 how old is Bill?
Sedaia [141]
Bill's age = x

Eya's age = 3x - 5

Eya is 28

28 = 3x - 5

28 (+5) = 3x -5 (+5)

33 = 3x

33/3 = 3x/3

x = 11

Bill = x

x = 11

Bill is 11 years old

hope this helps
4 0
3 years ago
Help me!! Thank you for the help!!
VLD [36.1K]

Answer:

D. 0.34

Step-by-step explanation:

0.24²+0.31²=x² then you find the square root

6 0
3 years ago
Read 2 more answers
8x(5+10)= (8x5) + (5x10)
Slav-nsk [51]

Answer:

i think its x= 0.75

Step-by-step explanation:

substitute:

8x × 5 = 40x

8x × 10 = 80x

8 × 5 = 40

5 × 10 =50

40x + 80x = 40 + 50

add like terms

so it'd be:

120x = 90

now divide 90 by 120 and that would give you the value of x alone which is 0.75

7 0
3 years ago
Read 2 more answers
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