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nekit [7.7K]
3 years ago
6

A carpenter has a piece of wood that is 78 inches long. He wants to cut it so that one piece is five times as long as the other

Mathematics
2 answers:
Lyrx [107]3 years ago
7 0

Answer:

13 and 65

Step-by-step explanation:

x + 5x = 78

(because u want a piece (x) and a piece that's five times longer than x- so 5x. and they should come from a 78 inch piece)

6x = 78

x = 78 / 6

x= 13

(to counter check:  13 * 5 = 65.  

                               65 + 13 = 78  )

Alona [7]3 years ago
5 0
One piece is 13, the bigger piece is 65!

we know this because if one piece is 13, the piece 5 times bigger is (65), and 65+ 13 is 78.
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Answer:

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Step-by-step explanation:

We are given the trigonometric equation of:

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Let u = 4x then:

\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

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Convert u-term back to 4x:

\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Divide both sides by 4:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

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