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sukhopar [10]
3 years ago
9

Find two numbers such that one exceeds the other by 11 and their sum is 73.

Mathematics
1 answer:
Whitepunk [10]3 years ago
5 0

Answer: 31 & 42

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

1st #: x

2nd #: x + 11

1st# + 2nd# = sum

 x    +  x + 11 =  73

         2x + 11 = 73

         2x        = 62

           x          = 31


2nd #: x + 11   = 31 + 11   = 42

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))
BartSMP [9]
By using <span>De Moivre's theorem:
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ \sqrt[n]{z} =  \sqrt[n]{a} \ (cos \  \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )
k= 0, 1 , 2, ..... , (n-1)


For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>

Part (A) <span>find the modulus for all of the fourth roots
</span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root = \sqrt[4]{z} =  \sqrt[4]{81} = 3

Part (b) find the angle for each of the four roots

The angle of the given complex number = \frac{3 \pi}{8}
There is four roots and the angle between each root = \frac{2 \pi}{4} =  \frac{\pi}{2}
The angle of the first root = \frac{ \frac{3 \pi}{8} }{4} =  \frac{3 \pi}{32}
The angle of the second root = \frac{3\pi}{32} +  \frac{\pi}{2} =  \frac{19\pi}{32}
The angle of the third root = \frac{19\pi}{32} +  \frac{\pi}{2} =  \frac{35\pi}{32}
The angle of the  fourth root = \frac{35\pi}{32} +  \frac{\pi}{2} =  \frac{51\pi}{32}

Part (C): find all of the fourth roots of this

The first root = z_{1} = 3 ( cos \  \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})
The second root = z_{2} = 3 ( cos \  \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})

The third root = z_{3} = 3 ( cos \  \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})
The fourth root = z_{4} = 3 ( cos \  \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})
7 0
3 years ago
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Sliva [168]

Answer:

A

Step-by-step explanation:

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3 years ago
Sara is 6 years older than max in 3 years she’ll be 1 1/2 of max’s age . how old is max ?
Andrews [41]
S = m+6
(s + 3) = (m + 3)1.5
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3 years ago
a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers starte
ankoles [38]

Answer:

<em>Worker B needs 9 days to finish the rest of the work</em>

Step-by-step explanation:

<u>Proportions</u>

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

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After 3 days they have completed:

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parts of the project, this means it still remains:

1-\frac{7}{16}=\frac{9}{16}

parts of the project and it is done by B alone. Since B does \frac{1}{16} per day, he now takes

\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9

days to complete the project.

Worker B needs 9 days to finish the rest of the work

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Answer:

29

Step-by-step explanation:

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