Answer:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Step-by-step explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Answer:
Step-by-step explanation:
39²=1521
80²=6400
39²+80²=1521+6400=7921
87²=7569
7921≠7569
so it is not aright angled triangle.
Step-by-step explanation:
y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1
dy/dx = 12√x
Arc length is:
s = ∫ ds
s = ∫₀¹ √(1 + (dy/dx)²) dx
s = ∫₀¹ √(1 + (12√x)²) dx
s = ∫₀¹ √(1 + 144x) dx
If u = 1 + 144x, then du = 144 dx.
s = 1/144 ∫ √u du
s = 1/144 (⅔ u^(³/₂))
s = 1/216 u^(³/₂)
Substitute back:
s = 1/216 (1 + 144x)^(³/₂)
Evaluate between x=0 and x=1.
s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]
s = 1/216 (145)^(³/₂) − 1/216
s = (145√145 − 1) / 216
20000*0.45 = 9000 in the bond
20000*0.15 = 3000 in the CD
20000*0.20 = 4000 in stocks
20000*0.029 = 580 in savings
A=9000(1 + 4.35%)^3 = 10,226.33
A=3000(1 + 2.90%)^3 = 3,268.64
A=4000 (1 + 8%) x (1 - 4%) x (1 + 6%) = 4,396.03
A=580(1 + 4.35%)^3 = 4,545.04
Total value = 22,436.04
Gain = 22,436.04 - 20,000 = 2,436.04
