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romanna [79]
3 years ago
8

if n is an integer, what is the sum of the next three consecutive even integers greater than 2n? a. 6n + 12 b. 6n + 10 c. 6n + 4

d. 6n + 8​
Mathematics
1 answer:
iogann1982 [59]3 years ago
8 0

Answer:

a) 6n + 12

Step-by-step explanation:

Next three consecutive integers are :  2n + 2 , 2n + 4 , 2n + 6

2n + 2 + 2n +4 +2n +6 = 2n+ 2n + 2n + 2 + 4 + 6

                                    = 6n + 12

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<h2>Answer:</h2>

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures 5\pi/12=75^{\circ}. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})

Finally, the exact value of the position of the rider after the carousel rotates 5\pi/12 radians is:

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

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