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Law Incorporation [45]
3 years ago
10

What is the total volume of glass used to make the award?

Mathematics
2 answers:
Sholpan [36]3 years ago
7 0
152 inches cubes because when I done this in my class he gave us the answer
alina1380 [7]3 years ago
3 0

Answer:

The answer is option 2.

Step-by-step explanation:

We have to seperate the figure into 2 shapes, pyramid and cube. Then you find the volume of each shapes. First, we will find the volume of pyramid using the formula, V = 1/3×base area×h where the base area is the area of the square and h is the height of pyramid :

base area = 6×4

= 24 in²

h = 15 - 2

= 13 in

V = 1/3×24×13

= 104 in³

Next you have to find the voulme of cube with the formula, V = l×b×h where l represents the length, b is breadth and h is the height :

l = 6 in

b = 4 in

h = 2 in

V = 6×4×2

= 48 in³

Lastly, you just have to add up both voulmes of the shapes together :

V pyramid = 104 in³

V cube = 48 in³

V figure = 104 + 48

= 152 in³

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We have to calculate the fourth roots of this complex number:

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Then, the exponential form is:

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The formula for the roots of a complex number can be written (in polar form) as:

z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})

We can now calculate for each value of k:

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Answer:

The four roots in exponential form are

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z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

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