3. In an experiment a scientist mixes together three substances. She mixes 18.42 g of
1 answer:
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Answer:
- A: $37500
- B: $17500
Step-by-step explanation:
Natsano can satisfy his constraints by investing the first $20,000 in Company A, then splitting the remaining $35,000 evenly between the companies. For best return, he needs to invest as much as possible in Company B, but each such dollar (after the first 20k) must be matched by a dollar invested in Company A. That is, his investments should be ...
- Company A: $37,500
- Company B: $17,500
_____
The attached graph shows the feasible region of investments (doubly shaded). The vertex that maximizes the objective function (return on investment) is the one highlighted. (It puts the objective function line as far as possible from the origin.)
_____
Sometimes graphing the constraints is more work than necessary if there is some simple logic that quickly identifies the solution.
Answer:
The translation did not effect the domain
The translation effected the range
Step-by-step explanation:
The given graph represents f(x) = IxI
The domain of f(x) is {x : x ∈ R}, where R is the set of real numbers
The range of f(x) is {y : y ≥ 0}
The graph of g(x) is attached down
g(x) = IxI + 4
The domain of g(x) is {x : x ∈ R}, where R is the set of real numbers
The range of g(x) is {y : y ≥ 4}
The graph of g(x) is the image of the graph of f(x) after translate it 4 units up
∵ The translation is vertically
∴ The domain of f(x) = the domain of g(x)
∵ The domain of f(x) is {x : x ∈ R}
∴ The domain of g(x) is {x : x ∈ R}
∴ The translation did not effect the domain
∵ g(x) = f(x) + 4
∵ The range of f(x) is {y : y ≥ 0}
- Add 4 to the value 0
∴ The range of g(x) is {y : y ≥ 0 + 4}
∴ The range of g(x) is {y : y ≥ 4}
∴ The range of g(x) not equal the range of f(x)
∴ The translation effected the range
