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3 years ago

The nature center has a fish tank

Mathematics

2 answers:

iren [92.7K]3 years ago

8 0

Answer:

288 small fish

Step-by-step explanation:

l=6

w=4

h=4

lwh=96 cub feet

3=1 cub feet

3x96=288

288 fish

ANEK [815]3 years ago

4 0

Answer:

288 small fish.

Step-by-step explanation:

The first thing is to calculate the volume of the prism, which would be the area of the base (length by width) and that by the height, that is:

a = l * w * h

l = 6

w = 4

h = 4

Replacing

a = 6 * 4 * 4

a = 96 cubic feet

they tell us that per cubic foot there is room for 3 small fish, therefore:

96 * 3 = 288

Which means that there are 288 small fish.

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Katarina [22]

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3 years ago

Rewrite 2sin2x + 3 cos x − 3 in terms of cos x

Feliz [49]

9514 1404 393

Answer:

-2cos²(x) +3cos(x) -1

Step-by-step explanation:

Use the "Pythagorean identity" to replace sin²(x).

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2 years ago

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

chubhunter [2.5K]

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3 $\sqrt$ 3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3 $\sqrt$ 3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48 $\sqrt$ 3]

Divide both sides by 0.04

275 = 24l + 48 $\sqrt$ 3

Subtract 48 $\sqrt$ 3 from both sides

24l = 275 - 48 $\sqrt$ 3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm