Answer:
k = 10
Step-by-step explanation:
The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...
... Sk = a1·(1 -r^k)/(1 -r)
For the given numbers, this is ...
... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)
Manipulating this to get the term containing k, we have
... 1 -(2/3)(118096/78732) = (1/3)^k
... 1/59049 = (1/3)^k
Taking logarithms, we get
... -log(59049) = -k·log(3)
... log(59049)/log(3) = k = 10
We need to know the dimension of the paving stone.
For example, the paving stone is shaped like a rectangular prism with the following dimension.
Length = 10 inches
Width = 3 inches
Height = 2 inches
Volume of a rectangular prism = Length * Width * Height
V = 10 in * 3 in * 2 in
V = 60 in³
60 in³ / 4 in³ = 15
cost of paving stone = 2.50 + .18(15) = 2.50 + 2.7 = 5.20 per paving stone.
Answer:
160 and 70
Step-by-step explanation:
The restrictions are:
1) x ≥ 0
2) number of lower bowl seats = 65% * 18500 = 12,025
=> x ≤ 12,025
3) y ≥ 0
4) number of upper bowl seats = 35% * 18500 = 6,475
=> y ≤ 6,475
It is not necessary to state that x + y ≤ 18,500 because it is included in the other restrictions.
D is wrong. It can't have 2 angles equal to or greater than 90.
2x + 116.6 = 180
2x = 180 - 116.6
2x = 63.4
x = 63.4/2
x = 31.7 Two of this size are the only possible answers.
