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3 years ago

What is the area of the regular octagon below? 9m

Mathematics

1 answer:

Feliz [49]3 years ago

8 0

Answer:

No diagram and no explanation what 9 is.

However, if it is an octagon with each side equal to 9 then

area = (# of sides * side^2) / (4 * tan (180 # of sides))

area = 8 * 9 * 9 / (4* tan (180 / 8)

area = 648 / 4 * 0.41421

area = 391.1059607446

answer is C

Step-by-step explanation:

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4 years ago

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$

$h = 5324 / s^2$

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top $s^2$

Side area 4sh

Total surface area $A = s^2 + 4sh$

We can substitute $h = 5324 / s^2$

$A = s^2 + 4s\frac{5324}{s^2}$

$A = s^2 + 21296/s$

To find the minimum of this function, we can take the first derivative, and set it to 0

$A' = 2s - 21296/s^2 = 0$

$2s = 21296/s^2$

$s^3 = 10648$

$s = \sqrt[3]{10648} = 22$

$h = 5324 / s^2 = 5324 / 22^2 = 11$

4 0

3 years ago