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Deffense [45]
3 years ago
13

Evaluate 6²-7²+8²-9²+..+998²-999²​

Mathematics
1 answer:
Llana [10]3 years ago
3 0

Answer:

-499,485.

Step-by-step explanation:

We can transform this to an arithmetic series by  working it out in pairs:

6^2 - 7^2 = (6-7)(6+7) = -13

8^2 - 9^2 = (8-9)*8+9) = -17  

10^2 - 11^2 = -1 * 21 = -21 and so on

The common difference is -4.

The number of terms in this series  is (998 - 6) / 2 + 1

= 992/2 + 1 = 497.

Sum of n terms of an A.S:

= n/2 [2a1 + (n - 1)d  

Here a1 = -13, n = 497, d = -4:

Sum = (497/2)[-26 - 4(497-1)]

= 497/2 * -2010

= -499,485.

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Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is co
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Answer:

The land that is covered with an irrigation arm of 370 ft is  430,084\ ft^2

Step-by-step explanation:

<u>Area of the circle</u>

Being r the radius of a circle, its area can be calculated as follows:

A=\pi\cdot r^2

The irrigation arm acts as the radius of the irrigation circle, thus r=370 ft. The land covered is the area under the irrigation arm, thus:

A=\pi\cdot 370^2

A=430,084\ ft^2

The land that is covered with an irrigation arm of 370 ft is  430,084\ ft^2

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3 years ago
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4 years ago
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Jennifer, Kate, and Lucy line up in random order for basketball practice. What is the probability that the girls will line up fr
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Need some help with the answer to the question
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(- 4, 27 )

Step-by-step explanation:

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8 0
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