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sweet-ann [11.9K]
3 years ago
6

A triangular prism container is full of water of 428 cubic cm. The water is 10 cm deep, what is the base area of the container?

Mathematics
1 answer:
Hatshy [7]3 years ago
3 0
<h3>The base area of triangular prism container is 42.8 cubic centimeter</h3>

<em><u>Solution:</u></em>

<em><u>The volume of triangular prism is given as:</u></em>

v = base\ area \times height

Given that,

A triangular prism container is full of water of 428 cubic cm

The water is 10 cm deep

Therefore,

v = 428 cubic cm

h = 10 cm

<em><u>Substituting the values we get,</u></em>

428 = base\ area \times 10\\\\base\ area = \frac{428}{10}\\\\base\ area = 42.8\ cm^2

Thus the base area of triangular prism container is 42.8 cubic centimeter

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We get;

y = a·x² + b·x + c

At y = 6, x = -2

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6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

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Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

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b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

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6 - 8 = -b

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b = 4·a

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The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

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Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

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