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lina2011 [118]
2 years ago
9

On an island there are 7 cities each 2 of them connected by a direct road they are building a 8th city they also want it to conn

ect with the other 7 existing cities how many roads will there be after they build the 8th city
Mathematics
1 answer:
Katarina [22]2 years ago
8 0

Answer:

After the 8th city is built there will be 28 roads between the cities

Step-by-step explanation:

The given parameters are;

The number of cities initially on the island = 7 cities

The number of roads between each 2 cities = 1 road

Therefore, we have the number of roads between the 7 cities are;

7 cities taking 2 at a time = ₇C₂

_7C_2 = \dfrac{7!}{(7 - 2)!\cdot 2!} = 21

The initial number of roads between the 7 cities = 21 roads

The number of roads, 'n' there will be after the 8th city is built is therefore;

n = _8C_2 = \dfrac{8!}{(8 - 2)!\cdot 2!} = 28

The number of roads there will be after the 8th city is built, n = 28 roads.

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uysha [10]

Answer:

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

Step-by-step explanation:

Given an arbitrary ellipse (x²/a²) + (y²/b²) = 1       (a, b > 0)

The parametrization can be as follows

x = -a*Sin(t)

y = b*Cos (t)

then

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

If  t = 0

α(0) = (-a*Sin(0), b*Cos (0)) = (0, b)

If  t = π/2

α(π/2) = (-a*Sin(π/2), b*Cos (π/2)) = (-a, 0)

If  t = π

α(π) = (-a*Sin(π), b*Cos (π)) = (0, -b)

If  t = 3π/2

α(3π/2) = (-a*Sin(3π/2), b*Cos (3π/2)) = (a, 0)

If  t = 2π

α(2π) = (-a*Sin(2π), b*Cos (2π)) = (0, b)

We can see the sketch in the pic.

7 0
3 years ago
Read 2 more answers
Sue's Fruit Stand sells 20 different types of fruits. The table below shows the numbers of fruits that have certain percentages
Ksenya-84 [330]

Answer:

The first histogram is the answer.

Step-by-step explanation:

Like any other questions, you can use the process of elimination to answer this question.

There are only one fruit that has a water content of 60 - 64 %

Right away you can eliminate the second answer choice.

There are two fruits that has a water content of 65 - 69 %

All the other three has the same thing

There are only two fruits that has a water content of 70 to 74 %

Right away answer choice three can be eliminated

There are 4 fruits that are 75 - 79 % full with water

Both has same thing

There are 9 friuts that are 80 - 84 % full with water

THERE ARE 2 FRUITS THAT CONTAIN 85 - 89 % water

THE ANSWER IS THE FIRST HISTOGRAM.

5 0
3 years ago
Find the x intercept and the y intercept of the graph of the equation <br> 2x+4y=8
maksim [4K]

Answer:

x-intercept: 4

y-intercept: 2

Step-by-step explanation:

finding the x-intercept:

first, substitute y = 0.

2x + 4 x 0 = 8

then, remove the 0.

2x + 0 = 8

then, divide both sides. 2x = 8

so, x = 4.

finding the y-intercept:

first, substitute x = 0.

then, solve.

2 x 0 + 4y = 8

so, y = 2.

3 0
3 years ago
a square window has a perimeter of (8x + 12) feet. Write an expression that represents the side length of the window. (in feet)
Harrizon [31]
8x+12=p so you would take away 12 from p making the equation 8x=p-12 and then divide that by 8 so the equation is x= p-12/8 ( x equals p minus 12 over 8)

7 0
3 years ago
Place decimal points in 34, 4, and 417 so that the sum of the three numbers is 7.97.
KIM [24]
3.4+0.4+4.17=7.97 you just have to try different combinations of different numbers with the decimals.
                                                             





8 0
3 years ago
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