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3 years ago

David assembles 12 circuit boards in 255 minutes. Amy assembles 9 circuit boards in 170 minutes. Who works at a faster rate?

Mathematics

2 answers:

Artyom0805 [142]3 years ago

4 0

I think Amy works at a faster rate.

Marat540 [252]3 years ago

4 0

It would be Amy, because Amy does about 18.8 boards per min and David does about 18.75 boards per min.

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2 years ago

I need help proving this ASAP

Ket [755]

Answer:

See explanation

Step-by-step explanation:

We want to show that:

$\tan(x + \frac{3\pi}{2} ) = - \cot \: x$

One way is to use the basic double angle formula:

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ \sin(x) \cos( \frac{3\pi}{2} ) + \cos(x) \sin( \frac{3\pi}{2}) }{\cos(x) \cos( \frac{3\pi}{2} ) - \sin(x) \sin( \frac{3\pi}{2}) }$

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ \sin(x) ( 0) + \cos(x) ( - 1) }{\cos(x) (0) - \sin(x) ( - 1) }$

We simplify further to get:

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ 0 - \cos(x) }{0 + \sin(x) }$

We simplify again to get;

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