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nadya68 [22]
3 years ago
11

Find the center and radius of the circle described by the equation x2 + y2 + 6x - 4y - 27 = 0.

Mathematics
1 answer:
Lesechka [4]3 years ago
5 0

Answer:

Step-by-step explanation:

hello :

x²+ y² + 6x - 4y - 27 = 0 means : (x²+6x+9)-9+(y²-4y+4)-4-27 =0

(x+3)²+(y-2)² = 40....standard form when the center is (-3 , 2) and radius √40

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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
Which linear inequality is graphed with y >x-2 to
jek_recluse [69]

Answer:

D

Step-by-step explanation:

It's D on Edge, hope this helps

3 0
3 years ago
Someone please help me. I will give you hella points I need this answer to like graduate type
PtichkaEL [24]

Answer:

  • $9 and $7

Step-by-step explanation:

<u>The first equation:</u>

  • x + 2y = 23

<u>The second equation:</u>

  • 2x + 3y = 39

<u>Convert to slope-intercept form:</u>

  • x + 2y = 23 ⇒ 2y = -x + 23 ⇒ y = -1/2x + 11.5
  • 2x + 3y = 39 ⇒ 3y = -2x + 39 ⇒ y = -2/3x + 13

<em>The graph is attached</em>

<u>Intersection point is (9, 7)</u>

  • Adult tickets cost $9
  • Child tickets cost $7

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3 years ago
Please help me <br><br> 6th grade math
Marta_Voda [28]

Answer:

Late response, sorry. It is 750 meters.

Step-by-step explanation:

An easy method to save time is to just divide the distance by time to find what amount per second it can run. In this case, you have 120 and 4 to work with. Divide and you'll get 30 meters per second. Then, multiply 25(your seconds) by 30(the meters it runs per second) to get your answer.

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Trina's Toy Company charges $0.85 per pound to ship toys.
S_A_V [24]
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