Answer:
<u>The sequence is</u>
- 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...
Each term is the sum of the consecutive numbers from 1 to that number.
<u>The nth term is the sum of the first n numbers:</u>
- aₙ = 1 + 2 + 3 + ... + n
- aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
- aₙ = n(n + 1)/2
1) The number of circles in the nth pile is n(n + 1)/2
2) When n tends to infinity the number of circles tends to infinity
Answer:
D
Step-by-step explanation:
Its D because A is all 90 degrees
Not C because all 90
Answer:
360 mi/h
Step-by-step explanation:
The speed for the outbound trip was ...
speed = distance/time = (715 mi)/(2 1/6 h) = 330 mi/h
The inbound speed was ...
(715 mi)/(1 5/6 h) = 390 mi/h
The airspeed of the plane is the average of these two ground speeds, so is ...
(330 +390)/2 = 360 . . . . mi/h
Answer:
60.25≈60.3°
Step-by-step explanation:
tanФ=14/8=1.75
Ф=arctan=1.75
tan-1
60.25≈60.3
Answer:
(48 m^12)/n^8
Step-by-step explanation:
Simplify the following:
3 ((2 m^3)/(n^2))^4
Multiply each exponent in (2 m^3)/(n^2) by 4:
3×2^4 m^(4×3) n^(-2×4)
4 (-2) = -8:
3×2^4 m^(4×3) n^(-8)
4×3 = 12:
(3×2^4 m^12)/(n^8)
2^4 = (2^2)^2:
(3 (2^2)^2 m^12)/(n^8)
2^2 = 4:
(3×4^2 m^12)/(n^8)
4^2 = 16:
(3×16 m^12)/(n^8)
3×16 = 48:
Answer: (48 m^12)/n^8
