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oksian1 [2.3K]
3 years ago
8

A piece of fabric is 2 yards long Marcus puts one patch at each end of the fabric and at each quarter foot mark how many patches

did Marcus use
Mathematics
2 answers:
loris [4]3 years ago
8 0

Answer:

Step-by-step explanation:

klio [65]3 years ago
5 0
Conversion.
1 yard = 3 feet

So the fabric has 2 yards. Then the size of the patch is 1/4 foot. 
So the number of patches that Marcus used is..
= 3 * 2
= 6 / (1/4)
= 24 patches.

So a total of 24 patches Marcus used.
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<img src="https://tex.z-dn.net/?f=%20%7B%20%5Ccos%5E%7B4%7D%5Calpha%7D%20%5C%3A%20%2B%20%20%20%5Csin%5E%7B2%7D%20%5Calpha%20%5C%
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Answer:

Proved

Step-by-step explanation:

cos^4\alpha +sin^4\alpha =\frac{1}{4}(3+cos4\alpha )\\\\

Take the Left Hand Side:

cos^4\alpha +sin^4\alpha\\\\(cos^2\alpha )^2+(sin^2\alpha )^2\\\\(\frac{1+cos2\alpha }{2})^2+(\frac{1-cos2\alpha }{2})^2  \\\\\frac{1+2cos2\alpha +cos^22\alpha }{4}+\frac{1-2cos2\alpha +cos^22\alpha }{4} \\\\

\frac{1+2cos2\alpha +cos^22\alpha +1-2cos2\alpha +cos^22\alpha }{4} \\\\\frac{2+2cos^22\alpha }{4} \\\\\frac{1+cos^22\alpha }{2} \\\\\frac{1}{2}(1+cos^22\alpha )\\\\

\frac{1}{2}(1+\frac{1+cos4\alpha }{2})

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Hence Proved!

The following identities were used are attached in an image

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