Answer:
10.39 ft²
Step-by-step explanation:
To answer the question, we need to know the following;
- A regular polygon is a polygon whose sides are equal
- A hexagon is a six sided polygon
- A regular hexagon is a polygon with six equal sides
In this case, the length of one side of the hexagon is 2ft
We are required to determine the area of the hexagon;
We need to determine the number of triangles we can divide an hexagon into triangles from its center, then determine the center angle of each triangle.
Center angle = 360° ÷ 6
= 60°
Therefore, we have six isosceles triangles whose base side is 2 ft in length and the one angle at the top is 60°
Dividing the a triangle into two we have two right angled triangle each with an angle of 30° and one of the shorter side as 1 ft.
Using trigonometric ratios we can determine the other side.
tan 30 = opp/adj. opposite is 1 side
Adj = 1 ft ÷ tan 30
= 1.732 ft
Therefore, the area of each triangle = 0.5 × 1 ft × 1.732 ft × 2
= 1.732 ft²
Therefore, the area of a hexagon = 6 × 0.5 × 1 ft × 1.732 ft
= 10.392 ft²
Thus, the area of the hexagon is 10.39 ft²
Answer:
B
Step-by-step explanation:
You can just move upper y equation and it will be:
6x+3(3x-5)=15
6x+9x-15=15
15x-15=15
15x=30
x=2
Answer:
x = 23.33 hr Rodriguez sprinkler
y = 26.66 hr Hill sprinkler
Step-by-step explanation: INCOMPLETE QUESTION
Requiered information:
the water output rate for both sprinkler families
We assume : Rodriguez family 40 lts/hr
Hill family 35 lts/ hr
Total water output 1900 lts
and total combined hours working is 50 hr
Let call "x" time in hours sprinkler of Rodriguez family worked
and "y" time in hours sprinkler of Hill family worked
Then if total output was 1900 lts
40*x + 35*y = 1900 and x + y = 50
We have a two equation system, solving
y = 50 - x ⇒ 40*x + 35 * ( 50 - x )
40x = 1750 - 35x
75 x = 1750 ⇒ x = 1750/75 ⇒ x = 23.33 hr
and y = 50 - 23.33 ⇒ y = 26.66 hr
Answer:
relative minimum
Step-by-step explanation:
From f^''(x) = 12x we can take the integration to find out what f'(x) is:
Furthermore, we can substitute x = 1 for f''(x) to find out whether it's positive or negative
f''(1) = 12*1 = 12 > 0
So if x=1 is a critical point of f'(x) and f''(x=1) > 0 then that point is a relative minimum point
Answer:
A = 2 cm²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = 
h (b₁ + b₂ )
where h is the distance between parallel sides and b₁, b₂ , the parallel sides
Here h = 1, b₁ = 3, b₂ = 1 , then
A = × 1 × (3 + 1) = × 4 = 2 cm²
