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Ganezh [65]
3 years ago
14

How many total circles will be used if there are 20 rows of circles? Show all calculations.

Mathematics
1 answer:
Rashid [163]3 years ago
3 0

Answer:

210

Step-by-step explanation:

As there is one circle in first row, 2 circles in 2nd row and three in third row, which clearly implies that the number of circles in each row is equal to the row number. So, we have to calculate sum of first 20 numbers to calculate the total number of circles.

n=20

Total Circles=(n(n+1))/2

=(20 (20+1))/2

=(20(21))/2

=  420/2

=210

So the total number of circles will be 210.  

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Decompose each velocity in its i and j - coordinates.


1) River's velocity


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2) Luke's velocity

5m/s, 60° east of north

5* sin(60°) i + 5*cos(60°) j = 4.33 i + 2.5 j


3) Resultant velocity

[3.5i + 0j] + [4.33i + 2.5j] = 7.83i + 2.5j


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3 years ago
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The sum of the first ten terms of a linear sequence is 145. the sum of the next ten term is 445. find the sum of the first four
chubhunter [2.5K]

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

S_n =\frac{n}{2}(2a+(n-1)d)

The sum of the first ten terms of a linear sequence is 145

⇒ S_{10} =\frac{10}{2}(2a+(10-1)d)

⇒ 145 = 5 (2a+9d)

⇒ \frac{145}{5} =2a+9d

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The sum of the next ten term is 445, so the sum of first twenty terms is

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⇒ S_{20} =\frac{20}{2}(2a+(20-1)d)

⇒ 590 = 10 (2a + 19d)

⇒ \frac{590}{10}=2a+19d

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Now subtract (2) from (1),

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⇒ d = \frac{30}{10}

⇒ d = 3

Substitute d in (1), we get

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⇒ S₄ = 22.

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Answer:

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Step-by-step explanation:

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So, we have:

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