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3 years ago

When a number N is rounded to the nearest ten, the result is 630, but when

Mathematics

1 answer:

MAXImum [283]3 years ago

4 0

Answer:

N = 625 to 634
N = 15000 or 24999

Step-by-step explanation:

Let N = abc

If ab = 62 then c could be any number between 5 to 9, it will round up to 630
If ab = 63 then c could be any number between 0 and 4, it will round down to 630

N = 15000 ≈ 20000
N = 24999 ≈ 20000

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The patriot diner sells 2 cheeseburgers and one soda for $11.00 and 3 hamburgersand 2 sodas for $18.00. What is the cost of a ch

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Answer: the cost of a cheeseburger is $4

Step-by-step explanation:

Let x represent the cost of one cheeseburgers.

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3 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

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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 = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
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Part (C): find all of the fourth roots of this

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The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

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