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Anna007 [38]
3 years ago
7

The common difference of an ap is -2 find its sum of first term is hundred and last term is -10 with full solution

Mathematics
1 answer:
mixer [17]3 years ago
4 0

Answer:

2520

Step-by-step explanation:

The n th term of an AP is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given a_{n} = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

S_{56} = \frac{n}{2} (a₁ + a₅₆ )

      = \frac{56}{2} (100 - 10) = 28 × 90 = 2520

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A boat sails on a bearing of 77 degrees for 135 miles and then turns and sails 207 miles on a bearing of 192 degrees. Find the d
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Answer:

193.53 miles

Step-by-step explanation:

Please see the diagram for understanding of how the angles were derived,

Applying Alternate Angles, ABO =77 degrees

The bearing from B to C is 192=180+12 degrees

Subtracting 12 from 77, we obtain the angle at B as 65 degrees.

We want to determine the boat's distance from its starting point.

In the diagram, this is the line AC.

Applying Law of Cosines:

b^2=a^2+c^2-2acCosB\\b^2=207^2+135^2-2(207)(135)Cos65^\circ\\b^2=37453.8654\\b=\sqrt{37453.8654} \\b=193.53\: miles

The distance of the boat from its starting point is 193.53 miles (correct to 2 decimal places).

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3 years ago
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Answer:

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6 0
2 years ago
Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 50 meters. What is the diagonal d
jolli1 [7]

Answer:

70.7 meters.

Step-by-step explanation:

We have been given that Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 50 meters.

Since we know that diagonal of a square is product of side length of square and \sqrt{2}. So we will find diagonal of our given square plaza by multiplying 50 by \sqrt{2}.

\text{Diagonal distance across the plaza}=50\times \sqrt{2}

\text{Diagonal distance across the plaza}=50\times 1.414213562373095

\text{Diagonal distance across the plaza}=70.71067811865475\approx 70.7

Therefore, diagonal distance across the plaza is 70.7 meters.


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If 15 x 332 = 4,980, then
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Answer:

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Step-by-step explanation:

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