Answer:
a. T1 = -4 , T2 = -4/3 , T3 = -4/9 , T4 = -4/27
b. It is converge
c. The sum to ∞ = -6
Step-by-step explanation:
a.
∵ Tn = -4(1/3)^(n-1)
∵ The lower n = 1
∵ The geometric series Tn = a(r)^(n-1)
∴ T1 = a , T2 = ar , T3 = ar² , T4 = ar³
∴ a = -4 , r = 1/3
∴ T1 = -4
∴ T2 = -4(1/3) = -4/3
∴ T3 = -4(1/3)² = -4/9
∴ T4 = -4(1/3)³ = -4/27
b.
r = 1/3
∴ -1 < r < 1
∴ It is converge because the value of 1/3 when n is a very large
number will approach to zero
c.
∵ The sum of the geometric series = a(1-(r)^n)/1-r
∵ r^n ≅ 0 when n is a very large number
∴ The sum to ∞ = a/1 - r = -4/(1 - 1/3) = -4/(2/3) = -6
<h3>
Answer: Yes it is a rational number</h3>
All terminating decimals are rational numbers
In this case,
3.12311 = 312311/100000
which shows that 3.12311 can be written as a ratio of two integers, therefore making it a rational number.
1/3 is 1 and 1 is 2 and 3 is 4 and 9 is 10
Answer:
44.1
Step-by-step explanation:
180-102-28=50
Sin(28°)/27=.0173
Sin(50°)/.0173=44.056
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Find x :
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Sum of adjacent angles on a straight line is 180.
∠ABY + ∠YBC = 180
x + 25 + 2x + 50 = 180
3x + 75 = 180
3x = 105
x = 35
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Check if AC is parallel to DF :
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If AC is parallel to DF,
∠YBC = ∠BEF (Corresponding angles)
∠YBC = 2x + 50 = 2(35) + 50 = 120
∠BEF = 5x - 55 = 5(35) - 55 = 120
Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer: Since ∠YBC = ∠BEF, AC and DF are parallel.
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