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taurus [48]
3 years ago
6

Find h. 11 in. h = [?] in in. 14 in. PLEASE OH PLEASE HELP ME IM DESPERATE

Mathematics
1 answer:
Sliva [168]3 years ago
4 0

11^2 = h^2 + ( 14/2)^2

11^2 = h^2 + 7^2

121 = h^2 + 49

h^2 = 121 - 49

h^2 = 72

h = √72

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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
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
andreev551 [17]

Answer:

816 square feet

Step-by-step explanation:

13(16+20+12) + 16(12) = 816

7 0
3 years ago
Which ordered pair is a solution of the inequality? 3y-6&lt;12x
BartSMP [9]
The answer is 3. (4, -2)
7 0
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How to multiply numbers with exponets and different bases
o-na [289]
When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:
a n ⋅ b n = (a ⋅ b) n
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144

When the bases and the exponents are different we have to calculate each exponent and then multiply:
a n ⋅ b m
Example:
32 ⋅ 43 = 9 ⋅ 64 = 576
5 0
3 years ago
What are the answer to both of these. I am confused. Please Help. I will give Brainliest Answer.
Mumz [18]

Answer:

The First 1 is B. And the Second 1 is B. As well.

Step-by-step explanation:

8 0
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