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dezoksy [38]
3 years ago
15

How do I solve 3x+2y=23 1/2x-4=y by using substitution?

Mathematics
1 answer:
mezya [45]3 years ago
8 0
In the second equation y= 1/2x -4. you take the 1/2x-4 and substitute it for y in the first equation. 3x+2(1/2x-4)= 23. So now you get 3x+x- 8=23. Now add the 3x and x together. 4x-8= 23.Now add 8 to both sides. 4x=31. Divide both sides by 4. x= 7 3/4 or 31/4 (its the same) Now take the 31/4 and put that as x in the second equation. 1/2(31/4)-4=y. 31/4-4=y. You get y=13/4 and x=31/4
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Find the sum \[\sum_{k = 1}^{2004} \frac{1}{1 + \tan^2 (\frac{k \pi}{2 \cdot 2005})}.\]
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\Rightarrow \sum_{k=1}^{2004}\left ( \frac{1}{1+\tan ^2\left ( \frac{k\pi }{2\cdot 2005}\right )}\right )

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Applying this we get

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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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Option (D) is correct

Step-by-step explanation:

If y is a multiple of x and versa, it will have a constant of proportionality.

Option (A)

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Option (B)

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Option (C)

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Option (D)

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In option (D), we see that x is 9 times of x. It means it has constant of proportionality equal to 9.

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