Express the number in scientific notation. 63,600,000
2 answers:
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Answer:
a) 3, 6, 9, 12, 15,...,, b) 4, 7, 10, 13, 16,...,
, c) Both sequences are arithmetic.
Step-by-step explanation:
a) The sequence of natural numbers which are multiplied by 3 are represented by the function ,
. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...
b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function ,
. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...
c) Both sequences since differences between consecutive elements is constant. Let prove this statement:
(i)
(ii)
Both sequences are arithmetic.
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W =
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
The work done in pulling half the rope, W₂ = 562.5 lb·ft