The first step of simplifying the expression would be summing up the "i"s. They are separate ("+i" and "+5i") but you can still sum them up though they are apart. This is thanks to the commutative property of addition which allows summing the terms of an expression with several additions in whatever order it is prefered. Commutative means that the terms can be interchangeable.
Answer:
C...........................
Answer:
Step-by-step explanation:
Using the exponential growth function for the U. S. population from 1970 through 2003:
A = 205.1e^0.011t
with the U.S. population being 205.1 million in 1970, when would the U. S. population reach 350 million?
A.
2028
B.
2048
C.
2018
D.
2038
We have the expression
A = 205.1e^0.011t
We are asked to find when would the U. S. population reach 350 million
A = 350
350 = 205.1e^0.011t
We divide both sides by 205.1
Divide both sides by 205.1
350/205.1 = 205.1e^0.011t/205.1
1.7064846416 = e^0.011t
We take the log of both sides
log 1.7064846416 = log e^0.011t
log 1.7064846416 = t log 0.011
t = log 1.7064846416/ log 0.011
t = 0.1185057826
Answer:
8. (-∞, 0) ∪ (0, 1/3) ∪ (1/3, ∞)
9. f(g(x)) = 4x/(1+6x)
Step-by-step explanation:
8. For f(g(x)) to be defined, g(x) must be defined and f(g(x)) must be defined.
g(x) will be defined for all x≠0. f(g(x)) will be defined for g(x)≠4. Solving g(x)=4, we find the value of x is 1/3. (The answer choices give a clue.)
So, the domain of f(g(x)) is all x that is not 0 or 1/3. Only one answer choice makes those particular exclusions:
(-∞, 0) ∪ (0, 1/3) ∪ (1/3, ∞)
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9. Substituting the definition of g(x) into the expression for f(x), we get ...
