I got x= -7. hope that helps you out!
Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
Answer:
let her animals be represented by y
then 5/100 x y=7
y=100/5 x7=140
Step-by-step explanation:
Answer:
height = 23 ft , Width=43ft
Step-by-step explanation:
Step one:
Given data
Given data
Diagonal = 66ft
Aspect ratio= 19:10
From the formulas below, we can find the dimensions of the theater screen
height = diagonal / √ (AR²+1)
where AR is the aspect ratio
Step two:
height = 66 / √ ((19/10)² + 1) =
height = 66 / 2.9
height = 23 ft
Step three:
Also,
width = AR * height
width = (19/10) * 22.75
width =1.9* 22.75
Width=43ft
Answer:
$1.935
Step-by-step explanation:
As the store is offering a 15% discount, you have to calculate the 15% of the price of the game app to find the amount of the discount:
Price of the game app= 12.90
12.90*15%=1.935
According to this, the answer is that the amount of the discount if you buy the game app during the sale is $1.935 and you would have to pay: 12.90-1.935= $10.965.
