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4 years ago

One exterior angle of a regular pentagon has a measure of (2x) what is the value of x

2 answers:

8 0

<span>Each Exterior Angle = (360 degrees) ÷ (Number of Sides)
</span>
A pentagon has 5 sides so

<span>Each Exterior Angle = 360 / 5
</span>
Each Exterior Angle =72
If the exterior angle = 2x and the angle = 72 degrees then
2x = 72 and
x = 36
Source:
http://www.1728.org/polygon.htm

NikAS [45]4 years ago

7 0

Answer:

x = 36° .

Step-by-step explanation:

Given : One exterior angle of a regular pentagon has a measure of (2x).

To find : what is the value of x.

Solution : We have given

One exterior angle of a regular pentagon has a = (2x).

Each exterior angle = $\frac{360}{number\ of\ exterior\ angle}$ .

Plug the values each exterior angle = 2x , number of exterior angle = 5.

2x = $\frac{360}{5}$ .

2x = 72.

On dividing both sides by 2

x = 36.

Therefore, x = 36° .

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

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Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

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∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

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