X - y = 4
1 answer:
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Answer:
Step-by-step explanation:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
Check attachment for better understanding
Answer:
B)313 ft
Step-by-step explanation:
Hello,I think I can help you with this
to solve this you need to find all the measures of the rigth triangle formed by Hailey, the boat, and the point on the surface of the sea just above the head of Hailey
Step 1
define
triangle
Hypotenuse=300 feet
opposite side=y
adjacent side=x
angle of depression =30°
Step 2
find the distances
so, the point on the surface of the sea just above hailey is 259.8076 ft from the boat
hailey is at a depth of 150 feet
Step 3
now,her partner is 25 feet directly below her,it is
partner's depth is =hailey is at a depth of 150 feet+25
Y=175
he is at the same distance from de boat ( horizontal),because it is the same point in the sea surface.
X=259.80
Step 4
to find the distance between the partner and the boat we can use
Pythagoras theorem
so, Hailey's diving partner is 313 ft away from the boat(B)
Have a great day.