Please help to 10. Thank you

Mathematics

1 answer:

lubasha [3.4K]3 years ago

7 0

Answer: i dont know is the ans

Step-by-step explanation:

You might be interested in

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 $\theta$ there exist $\pi -\theta$

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

therefore

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

6 0

3 years ago

Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a

Artyom0805 [142]

According to the information presented, Benny should decide not to add a second chair because the average number of clients waiting is 1 (very low), the average waiting time for a client is 10 minutes (very low), and the average time a customer is in the store is 20 minutes (very low).

According to the information, an average of 2 clients arrive at the hairdresser for every hour (60 min) and each cut takes a maximum of 20 minutes. Therefore, the hairdresser would have an average of 40 minutes busy and 20 minutes free for each hour.

Additionally, customers who must wait do not have to spend a long time waiting in the store because the maximum waiting time is 10 minutes (in the case that both customers arrive at the same time).

Below is a graph where the information of both cases is compared (with an additional chair and without an additional chair) and it is inferred that an additional chair is not necessary because the number of clients waiting and the waiting time is not high.

Learn more in: brainly.com/question/25400126