Answer:
Expand it.
(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).
Multiply everything out (being sure to multiply <em>every</em> term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.
i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:
1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):
(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.
Simplify again, and the answer is: -11-2i
Step-by-step explanation:
I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.
Answer:
2(2x-1)/x(x-4)
Step-by-step explanation:
4x^2-14x+6/x^3-7x^2+12x
2(2x^2-7x+3)/x(x^2-7x+12)
2(2x^2-6x-x+3)/x(x^2-4x-3x+12)
2(x-3)(2x-1)/x(x-4)(x-3)
Answer:
p(t) = 100%·2^(-t/1.32)
Step-by-step explanation:
The equation for exponential decay is ...
(remaining amount) = (initial amount)·2^(-t/(half-life))
Here, we can represent the percentage remaining by p(t) and the initial amount by 100%. Then, for a half-life of 1.32 minutes, the amount remaining is ...
p(t) = 100%·2^(-t/1.32) . . . . . where t is in minutes
_____
Alternate functional forms are possible, such as ...
p(t) = 100%·e^(-0.525112t)
p(t) = 100%·0.591489^t
Step-by-step explanation:
S = ∫ 2π y ds
ds = √(1 + (dx/dy)²) dy
ds = √(1 + (8y)²) dy
ds = √(1 + 64y²) dy
S = ∫₁² 2π y √(1 + 64y²) dy
S = π/64 ∫₁² 128y √(1 + 64y²) dy
S = π/64 [⅔ (1 + 64y²)^(³/₂)] |₁²
S = π/96 (1 + 64y²)^(³/₂) |₁²
S = π/96 (1 + 256)^(³/₂) − π/96 (1 + 64)^(³/₂)
S = π/96 (257√257) − π/96 (65√65)
S = π/96 (257√257 − 65√65)
