Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
Answer:
y=-2x+7
Step-by-step explanation:
To find "c" put one of the points in the equation. Put$(3,1)$
$1=-2(3)+c$
$c=1+6=7$
Answer:
C
Step-by-step explanation:
Adding we get:
-2x^2+3x^2 + 7x - 8x - 6 -1 = X^2 -x-7
Answer:
113.09734
Step-by-step explanation: