ABCDEFGH is a regular octagon. The minimum degree of rotation by which this octagon can map onto itself is (30 ; 45 ; 90 ; 120 °
). It will take ( 2 ; 4 ; 6 ; 8 ) increments of that degree of clockwise rotation for A′ (the image of A) to coincide with C.
2 answers:
Answer:
45°
2 - Clockwise
Step-by-step explanation:
ABCDEFGH is a regular octagon.
The minimum degree of rotation by which this octagon can map onto itself.
For rotation we have to find the central angle of each side.
Complete angle = 360°
A regular octagon has 8 equal sides. All sides make same angle at center.
8Ф = 360°
Ф = 45°
If we rotate regular octagon by 45° then it map onto itself.
Hence, 45° correct answer.
After 2 times clockwise rotation by 45° each time. We will get the image of A coincide with C as shown in attach figure.
C is second vertex of A.
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Given:
Volume of a cubed room = 8000 cubic ft
Cost of floor hardwood = $10 per square foot
To find:
The total cost of floor hardwood.
Solution:
Let the each side of cubed room be x ft.
Volume of a cube is cube of its side.
Volume of a cubed room is 8000 cubic ft. So,
Taking cube root on both sides.
So, length of each of room is 20 ft.
Area of base = length × breadth
So, area of base of room is
It means, 400 sq ft hardwood is required for the floor.
Cost of floor hardwood is $10 per square foot. So, total cost of hardwood floor is
The hardwood floors will cost $4000.