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soldier1979 [14.2K]
4 years ago
6

8,205,000 in expanded form

Mathematics
1 answer:
const2013 [10]4 years ago
8 0
8,000,000 + 200,000 + 5,000
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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                          

6 0
3 years ago
Punam receives Rs. 3040 as commission for selling goods at Rs. 34000. What is commission rate?​
NISA [10]

Answer:

8.9411%

Step-by-step explanation:

x

------ × 34000 = 3040

100

34000x = 304000

x = 304000

---------------

34000

x = 8.94

4 0
3 years ago
What is the upper and lower quartile of this set of data? 15, 19, 20, 25, 31, 38, 41
aev [14]
Answer:

Upper quartile: 38
Lower quartile: 19
3 0
3 years ago
Read 2 more answers
Which equation represents the line that passes through (-5,-2) and has a slope of 3
MrRa [10]

You already know the slope is 3 and you have the point, so you would plug it into y = mx + b

-2 = y

3 = m

-5 = x

Plug in:

-2 = 3(-5) + b

Solve:

-2 = -15 + b

-2 (+15) = -15 + b (+15)

13 = b

Now you have b, so you can form the equation where the slope is 3x and the y-intercept is 13.

Final answer: y = 3x + 13


8 0
3 years ago
Liam is a tyre fitter it takes him 56 minutes to fit 4 tyres to a van if he works for 42 minutes how many tyres can he fit.
dlinn [17]
I think the answer is 2 tyres but i am not sure but don’t blame me if it’s wrong
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3 years ago
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