Answer:
700 lei
Step-by-step explanation:
You have a geometric sequence for which you know the common ratio and the last term.
There are only three terms, so you can solve the problem in either of two ways.
1. The brute force method
(easiest for only a few terms)
Each term is half the one before it, so each term is double the one after it.
3rd term = 100 lei
2nd term = 200
1st term = 400
Total = 700 lei
Oana spent 700 lei
2. Using formulas (best for longer sequences)
The general formula for your sequence is
aₙ = a₁rⁿ⁻¹
For your sequence,
a₃ = 100; r = 0.5
(a) Calculate a₁
Set the last term equal to the general formula.
a₃ = a₁(0.5)ⁿ⁻¹
100 = a₁(0.5)² = 0.25a₁
a₁ = 100/0.25 = 400
(b) Calculate the sum
The general formula for the sum of a geometric sequence is
Oana spent 700 lei.
Answer:
d. 36 sq. ft
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 (12) * 6
A = 36 ft^2
Answer:
x = 2, y = 5
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, thus
PT = TR and QT = TS
Substitute in values
y = 2x + 1 → (1)
3y = 3x + 9 → (2)
Substitute y = 2x + 1 into (2)
3(2x + 1) = 3x + 9
6x + 3 = 3x + 9 ( subtract 3x from both sides )
3x + 3 = 9 ( subtract 3 from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
Substitute x = 2 into (1)
y = 2(2) + 1 = 4 + 1 = 5
Answer:
54.514 rev/min
Step-by-step explanation:
Data provided in the question:
Speed of the cable car = 12.65 miles per hour
Diameter of the rotating wheel, d = 6.5 feet
Now,
The speed of rotation of the wheel will be equal to the speed of the cable car
thus,
The speed of rotation of the wheel = 12.65 miles per hour
also,
1 miles = 5280 feets
1 hour = 60 minutes
Thus,
The speed of rotation of the wheel = 
= 1113.2 ft/ min
Circumference of the wheel = πd
= 6.5π feet
= 20.42 feet
Therefore,
The speed of rotation of the wheel in revolutions per minute
= 1113.2 ÷ 20.42 rev/min
= 54.514 rev/min
