Answer: r = 2/3
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = 36
The 4th term is 32/3
n = 4
Therefore,
T4 = 32/3 = 36 × r^(4 - 1)
32/3 = 36 × r^3
Dividing both sides if the equation by 36, it becomes
32/3 × 1/36 = r^3
8/27 = r^3
Taking cube root of both sides of the equation, it becomes
(8/27)^1/3 = r^3 × 1/3
r = 2/3
Step-by-step explanation:
hope it will helps you my answer
Answer:
10 years
Step-by-step explanation:
We are told that One year after you buy a tree, it is 10 feet tall. Thus, it's initial height after 1 year is 10 ft.
Now we are told that each year after you buy the tree, it grows 2 feet. This means that it's height after you bought it was; f(0) = 10 - 2 = 8ft
Thus,
f(1) = 8 + 2 = 10
f(2) = 8 + 2 + 2 = 12
f(3) = 8 + 2 + 2 + 2 = 14
The pattern here is;
f(x) = 8 + 2x
Where x is number of years
Thus, for it to reach a maximum height of 28 ft;
28 = 8 + 2x
Subtract 8 from both sides to give;
28 - 8 = 2x
2x = 20
x = 20/2
x = 10 years
First, we solve for the equation of the line using the two-point formula:
(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)
The coordinates are:
(1,-1)
(3,0)
(y - (-1)) / (x - 1) = (0 - (-1)) / (3 - 1)
y = 0.5x - 1.5
Since the line is dotted, it's a strict inequality and since the portion below the line is shaded, we use the inequality, less than.
y < 0.5x - 1.5
In standard form:
x - 2y > 3
The answer is the first option.
