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blsea [12.9K]
3 years ago
8

Which of the following is the general term for the sequence

Mathematics
1 answer:
umka21 [38]3 years ago
6 0
The first one and it's written as a(-1)(n-1). The parenthesis around the n-2 are important
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Answer:

1. The speed of the truck, S = D/T.

2. The formula that connects D and T is: S = D/T.

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a) The speed of a truck at a fixed speed is given as the distance covered by the truck divided by the time it takes the truck to cover the said distance.  This implies that speed is a function of distance and time.  However, this formula represents the mean speed.  There are variations in speed.

b) If the truck covers a distance of 60 kilometers, for example, under 3 hours, we can conclude that the speed is 20 kilometers per hour (60/3) or 20 km/hr.

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Find the sum \[\sum_{k = 1}^{2004} \frac{1}{1 + \tan^2 (\frac{k \pi}{2 \cdot 2005})}.\]
vampirchik [111]

Answer:1002

Step-by-step explanation:

\Rightarrow \sum_{k=1}^{2004}\left ( \frac{1}{1+\tan ^2\left ( \frac{k\pi }{2\cdot 2005}\right )}\right )

and 1+\tan ^2\theta =\sec^2\theta

and \cos \theta =\frac{1}{\sec \theta }  

\Rightarrow \sum_{k=1}^{2004}\left ( \cos^2\frac{k\pi }{2\cdot 2005}\right )

as \cos ^2\theta =\cos ^2(\pi -\theta )

Applying this we get

\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]

every \thetathere exist \pi -\theta

such that \sin^2\theta +\cos^2\theta =1

therefore

\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]=1002                          

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The tax should be $14242.5
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