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Morgarella [4.7K]
3 years ago
11

Ben put $60 into his savings account each month for years. He spent 60% of his savings on a used car. How much money did Ben hav

e left in his savings account after purchasing the car?
A.
$1,512.00
B.
$2,520.00
C.
$4,032.00
D.
$1,008.00
Mathematics
1 answer:
Vinil7 [7]3 years ago
3 0
A because I don’t know why
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Step-by-step explanation:

This problem does not specify what the radius of the circle is, and so we will have to represent that by r.

Arc length = s = rФ, where Ф is the central angle in radians.

Converting 162° into radians:  

162°        1 rad

------- · ------------ = 0.9 rad

    1        180°

Then the arc length BC is s = rФ, or r(0.9 rad)

If, for example, r = 10 m, then the arc length would be (10)(0.9) m = 9 m

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Give the domain and range of the relation (10,-3),(12,3),(-8,-7),(6,-1)
Iteru [2.4K]

Domain: {10, 12, -8, 6}

Range: {-3, 3, -7, -1}

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This relation is a function.

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What is 2 1/2 ft × 3 1/2 ft
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1 1/2

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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
4 years ago
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