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GenaCL600 [577]
3 years ago
10

Use​ Gauss's approach to find the following sums​ (do not use​ formulas). 1+3+5+7+...999

Mathematics
1 answer:
muminat3 years ago
4 0
S=1+3+5+\cdots+995+997+999
S=999+997+995+\cdots+5+3+1
\implies 2S=(1+999)+(3+997)+(5+995)+\cdots+(995+5)+(997+3)+(999+1)

2S=\underbrace{1000+1000+\cdots+1000+1000}_{500\text{ times}}

(We are adding 500 instances of 1000 because that's how many odd numbers there are between 1 and 1000, inclusive.)

2S=500\times1000=500000
\implies S=250000
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AVprozaik [17]
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7 0
3 years ago
Use the arc length formula and the given information to find r. s = 12 cm, 0 = 360; r = ?
hjlf
use s=r0

but first convert 360 degree to radian
you will get 6.284 radian

then you substitute and get the answer!

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8 0
2 years ago
18. You are standing beside the Colorado River, 400 feet
Veseljchak [2.6K]
<h3>Answer: B. 781.6 feet approximately</h3>

=======================================================

Work Shown:

The horizontal portion is 400+166 = 566 feet. Label this as 'a', so a = 566. The vertical side is unknown, so b = x. The hypotenuse is c = 965

Use the pythagorean theorem

a^2+b^2 = c^2

566^2+x^2 = 965^2

x^2 = 965^2 - 566^2

x = sqrt( 965^2 - 566^2 )

x = 781.58108984289 which is approximate

x = 781.6 feet when rounding to one decimal place

6 0
3 years ago
A cruise ship can cover 19 nautical miles in 323 minutes. How many nautical miles will it travel in 102 miles?
kow [346]
1 mile is equal to 0.868976 nautical miles
Therefore 12 miles is equal to 10.427, rounded the answer is B. 

Hope that was helpful.
4 0
3 years ago
How many 3-digit numbers can you write using only the digits 1 and 2?
defon
For the first digit, you have two possible choices: 1 or 2. For *each* of those choices, you can choose 1 or 2 for the second digit in the number, and for each of *those*, you can choose 1 or 2 for the third digit of the number.

That’s 2 * 2 * 2 or 8 possible 3-digit numbers you can make with the digits 1 and 2.
4 0
3 years ago
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