Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
The values of y get closer to the axis...
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
Step-by-step explanation:
The measure of the floor of the rectangular room that is 12 feet by 15 feet. The formula for determining the area of a rectangle is expressed as
Area = length × width
Area of the rectangular room would be
12 × 15 = 180 feet²
The tiles are square with side lengths 1 1/3 feet. Converting 1 1/3 feet to improper fraction, it becomes 4/3 feet
Area if each tile is
4/3 × 4/3 = 16/9 ft²
The number of tiles needed to cover the entire floor is
180/(16/9) = 180 × 9/16
= 101.25
102 tiles would be needed because the tiles must be whole numbers.
