An artist can sell 20 compies of a painting for $100 each, but for each additional copy he makes the value of each painting will
go down by 1 dollar. How many copies should he make to maximize the profit?
1 answer:
Answer:
40 copies for $3000
Step-by-step explanation:
First: The Equation
y=(20+x)(100-x)
This shows how for every new painting, the price will go down.
y=2000+80x-x²
Convert it to standard form: ax²+bx+c
You can now choose to graph it or find the vertex form. For the limit of time, I will just use a graph.
The vertex, (40,3000), is your answer, where the x value is the number of paintings and the y value the money made.
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Begin with the right hand side:
R.H.S = cot θ =
L.H.S = sin θ cos θ
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So, the equation is not a trigonometric identity.
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<u>Anther solution:</u>
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Assume θ with a value and substitute with it.
Let θ = 45°
So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2
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So, L.H.S ≠ R.H.S
So, sin θ cos θ = cot θ is not a trigonometric identity.