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)
Answer:
Step-by-step explanation:
the answer cannot be 5. Why? Because the minimum will occur when 12 and 5 point in opposite directions like both are on the x axis pointing to 0 from the east and pointing to zero coming from the west.
12 - 5 = 7
You cannot get a result less than that.
Answer:
C
Step-by-step explanation:
the equation of the parabola is : y = x² - 3x
the equation of the line is y = x + 1
and the shaded area is between those graphs
therefore y ≥ x² - 3x and y ≤ x + 1
Answer:
P= Rs 60000
A= Rs 79860
T=1 & 1/2 year = 3/2 years
= 3/2 x 2 = 3 half years
R= ?
Applying the formula A= P (1+r/100)^T
79860 = 60000 (1+ r/100)^3
79860/60000 = (1+r/100)^3
1331/1000 = (1+r/100)^3
root(3)(1331/1000) = (1+r/100)
11/10 = 1+r/100
11/10 -1 = r/100
1/10 = r/100
r= 10 %
Step-by-step explanation:
Answer:
D) 4.01 miles
Step-by-step explanation:
2.87 miles from Monday + 1.14 miles =4.01 ran on Tuesday
