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pentagon [3]
3 years ago
6

Three friends each have some ribbon.Carol has 42 in of ribbon,tino has 2.5 feet of ribbon, and baxter has 1.5 yards of ribbon. E

xpress the total length of ribbon the three friends have in inches, feet, and yards
Mathematics
1 answer:
Alexeev081 [22]3 years ago
7 0
Hello! This is simple. All you have to do is know the conversions. So, there are 12 inches in a foot, there are 36 inches in a yard, and there are 3 feet in a yard. So, we will start with feet. If there are 12 inches in a foot then you simply divide 42 by 12 which gives you 3.5 feet. Then you have to add the other 2.5 feet to it which gives us 6 feet. Lastly, you want to convert the yards into feet which is 4.5 feet. We just add all that together which gives us: 10.5 feet! 

Now let's do inches. So we leave the 42 alone since it is already in inches. Remember there are 12 inches in a foot, and there are 2.5 feet. So that gives us 30 inches. 42+30. Then we have 1.5 yards and there are 36 inches in a yard, so we divide which gives us 54 inches. So we have: 42+30+54= 126. So there are 126 inches.

Now that we have those out of the way, let's do yards. 2.5 feet in yards is 0.8 yards. So we have 0.8. Then we have 42 inches which is 3.5 feet. So then we figure that 3.5 is 1.1 yards so then we have 0.8+1.1+1.5= 3.4 yards!

So you get: 10.5 feet, 126 inches, and 3.4 yards!

I hope this helped!

I am, yours most sincerely,
SuperHelperThingy
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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))
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Part (A) <span>find the modulus for all of the fourth roots
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<span>∴ The modulus of the given complex number = l z l = 81
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∴ 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}
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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})
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evablogger [386]
ANSWER

x = 50.5 \degree

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


\frac{ \sin(A) }{a}  =  \frac{ \sin(B) }{b}  = \frac{ \sin(C) }{c}


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