SOLUTION:
The best graph that fit the given description is option A
Answer:
Step-by-step explanation:
Givem the profit function
p(x) = −2000x2 + 18000x − 15000
We are to generate the price range that will generate a monthly profit of at least $25,000
Substitute into the function we have;
25000 = −2000x2 + 18000x − 15000
Divide through by 1000
25 = -2x²+18x-15
Rearrange
-2x²+18x-15-25 = 0
2x²-18x+40 = 0
Divide through by 2
x²-9x+20 = 0
Factorize
x²-5x-4x+20 = 0
x(x-5)-4(x-5) = 0
x-4 = 0 and x-5 = 0
x = 4 and x = 5
Hence the price range that will generate a monthly profit of at least $25,000 is between $4 and $5 inclusive
Use the quadractic formula
The law of cosines is used for this purpose. It tells you
c² = a² + b² - 2ab×cos(C)
Solving for the angle C gives
C = arccos((a² + b² - c²)/(2ab))
C = arccos(( 17² + 15² - 19²)/(2×17×15))
C = arccos(153/510)
C ≈ 72.5424°
The measure of the angle opposite the longest side is about 73°.
cot(<em>x</em>) = cos(<em>x</em>) / sin(<em>x</em>)
so
cos(<em>x</em>) / cot(<em>x</em>) = 1 / (1/sin(<em>x</em>)) = sin(<em>x</em>)
Then
sin²(<em>x</em>) + sin(<em>x</em>) cos(<em>x</em>) / cot(<em>x</em>) = sin²(<em>x</em>) + sin²(<em>x</em>) = 2 sin²(<em>x</em>)
