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2 years ago

Hermie cuts out 60% of the shapes from his paper. He cut out 12. Enter the number of shapes on Hermie's paper.

Mathematics

1 answer:

pentagon [3]2 years ago

6 0

Answer:

Step-by-step explanation:

12 = 60% of x = 0.6x

x= 12/0.6= 20

Paper had 20 shapes. He cut out 12 shapes; 8 shapes remain

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vampirchik [111]

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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

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

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

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