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kirill115 [55]
3 years ago
9

Find four consecutive odd integers with a sum of 200

Mathematics
1 answer:
djyliett [7]3 years ago
7 0

Answer:

47, 49, 51, 53

Step-by-step explanation:

I don't know how your teacher wants you to do it, but the formula for odd integers in this case would be (n+1) + (n+3) + (n+5) + (n+7) = 200.

The four odd integers are represented by each set of parentheses. If we find n, we can add 1, 3, 5, and 7 to it to get the four numbers you're looking for.

If we subtract all of the constants from the left side and add all every n, we get 4n = 184. We then divide both sides by 4, and the answer is n = 46.

(n+1) = 47, (n+3) = 49, etc.

Hope this helps!

-Lacy

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Answer:

See Explanation Below

Step-by-step explanation:

Given

(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.

Required

Prove

To start with; we open the bracket on the left hand side

(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)

(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)

(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x

(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x

Reorder

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

From trigonometry;

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Also from trigonometry;

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