Answer:
where is simplify question
Notice that the pattern is "previous term plus 2". This is an arithmetic sequence where the difference (d) equals +2
= a₁ + d(n - 1) ; where a₁ is the first term, d is the difference, and n is the term.
f(n) = 1 + 2(n - 1)
f(n) = 1 + 2n - 2
f(n) = 2n - 1
********************************
f(10) = 2(10) - 1
f(10) = 20 - 1
f(10) = 19
A₀ = 18 000(1 + 0.0025)⁰
A₁ = 18 000(1 + 0.0025)¹
A₂ = 18 000(1 + 0.0025)²
A(n) = 18 000(1 + 0.0025)ⁿ
So, after 5 months, A(n) = 18 000(1 + 0.0025)⁵ = $18 226.1278 ≈ 18 226.13
5 years is 60 months.
A₆₀ = 18 000(1 + 0.0025)⁶⁰ = $20 909.1021 ≈ $20 909.10
Formula for the perimeter of a quarter circle: C = ((pi x 2r) / 4) + 2r
C = ((3.14 x 18) / 4) + 18
C = (56.52 / 4) + 18
C = 14.13 + 18
C = 32.13 miles
Hope this helps! :)
1a) Possible rational roots will be of the form
±{divisor of 10}/{divisor of 4}
Divisors of 10 are {1, 2, 5, 10}
Divisors of 4 are {1, 2, 4}
Then possible rational roots are
{±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10}
1b) Your answer is correct.
2) One additional root will be the conjuate of the given complex root.
5 -3i
3) If one root is 5 -√7, another will be 5 +√7. Then your polynomial is
P(x) = (x -(5 -√7))*(x -(5 +√7)) = (x -5)^2 -(√7)^2
P(x) = x^2 -10x +18
