0.076 but if you need to round its 0.08
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Suppose the shorter leg is x, then the longer leg is x+3, and the hypotenuse is x+6
x^2 +(x+3)^2 =(x+6)^2
x^2 + x^2 + 6x +9=x^2 + 12x +36
x^2-6x-27=0
(x+3)(3-9)=0
x=-3, which is impossible, or x=9
so the shorter leg is 9mm, the longer leg is 12mm, and the hypotenuse is 15mm
Answer:
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Step-by-step explanation:
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Answer:
1. $6.20
2. Samantha has $79, she decides to go to the mall and buys 6 dresses that are $7 each. She thinks that she might not have enough money so she returns 2 dresses. She then finds out that she has more than enough so she buys a candy bar for $5. How much money does she have left?
Sam has $79, she buys 6 dresses that cost $7 each. She returns 2 dresses and then buys a candy bar for $5. How much money does she have left?
Step-by-step explanation:
1. you can write an equation to represent the word problem
20-(2.10+0.9x)
20-(2.10+0.9(13)
20-(2.10+11.7)
20-(13.8)
6.2