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Rudik [331]
3 years ago
12

An Angle whose measure is 40 is in standard position. In which quadrant does the terminal side of the angle fall?

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
6 0

ANSWER

First quadrant

EXPLANATION

An angle in standard position starts measuring from the positive x-axis anticlockwise.

Since 40° is less than 90°, it's terminal side will fall within the first quadrant.

Hence the terminal side of a 40° is in the first quadrant.

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There are \dbinom{10}2 ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are \dbinom83 ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's \dbinom55=1 way of doing that.

So we have

\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520

The last expression has a more compact form in terms of the so-called multinomial coefficient,

\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520

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