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Delicious77 [7]
3 years ago
5

Let a = 3 – 5i and b = –1 + 7i. Which of the following are true statements? Check all that apply.

Mathematics
1 answer:
Alona [7]3 years ago
7 0

Answer: 2nd and 6th options are correct

Step-by-step explanation: It showed me after I got em wrong

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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
For the right triangle shown, the lengths of two sides are given. find the third side. leave your answer in simplified, radical
Citrus2011 [14]
There is no diagram
6 0
2 years ago
Help please!<br> -x - (-15) + -3.5x + 15
mrs_skeptik [129]
It would be 30 + 4.5x
7 0
3 years ago
Read 2 more answers
Solve the given system of equations2y=x+93x-6y=-15
attashe74 [19]

Answer:

No solutions

Explanation:

The given system of equations is

2y = x + 9

3x - 6y = -15

To solve the system, we first need to solve the first equation for x, so

2y = x + 9

2y - 9 = x + 9 - 9

2y - 9 = x

Then, replace x = 2y - 9 on the second equation

3x - 6y = -15

3(2y - 9) - 6y = -15

3(2y) + 3(-9) - 6y = -15

6y - 27 - 6y = -15

-27 = -15

Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.

5 0
8 months ago
What is the slope of the line? *<br><br> 3<br> 2<br> 6<br> 5<br> other: _______
timurjin [86]

Slope = (y2 - y1)/(x2 - x1)

Slope = (6 -0)/(3 - 0)

Slope = 6/3 = 2

Answer

2


8 0
3 years ago
Read 2 more answers
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