2/3(3x-15y)+(9y-11x)
1 answer:
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Answer:
f(x) = 10500sin(π/6(x -3)) +39500
Step-by-step explanation:
The average of the maximum and minimum revenue is the vertical offset of the function, parameter D.
D = (50,000 +29,000)/2 = 39,500
The amplitude of the function is the difference between the maximum and the offset.
A = 50,000 -D = 50,000 -39,500 = 10,500
The horizontal scale factor B is a number that will be equal to 2π when x-C = 12:
12B = 2π
B = π/6 . . . . . . divide by 12
The horizontal offset is such that revenue is neutral and increasing at the value x=C. That will be in the month of March, when x=3, so C=3.
Now we have all the parameters, so we can write the equation:
f(x) = 10500sin(π/6(x -3)) +39500
Answer: The correct answer is: " 9.3 hours " .
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Step-by-step explanation:
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To calculate:
Let "gal" represent "gallons (of gas)" ;
Let "h" represent "hour(s)" ;
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5 gal * ( <u> 1 h </u> ) = ? h ;
( 5/9 gal ) ;
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<u> Note</u>: On the "left-hand side" of the equation;
The units of "gal" ["gallons"] — "cancel out" ;
→ {since: "gal/ gal = 1"} ;
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and we can rewrite our equation as:
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( 5 )
________ hours ;
( 5/9 )
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To solve:
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5 1/6 ÷ (5/9) =
5 1/6 * (9/5) ;
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<u>Note</u>: Dividing by a fraction is the same as multiplying by that very fraction's reciprocal form.
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Now, let us convert "5 1/6" ; which is a "mixed fraction" ; into an
"Improper fraction" ;
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To do this, we can use the "MAD" method:
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M: Multiply the "denominator number" of the "fraction portion" [within the "mixed fraction"]—by the "whole number" [within the "mixed fraction" ; In this case: "6" , multiplied by "5" ; to get "30" ;
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Then:
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A: Add this obtained value; to the "numerator number" of the
"fraction portion" [within the "mixed fraction"] ;
In this case: "30" ; added to "1" ; to get 31:
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Then:
D: Divide this number by the "denominator number" of the "fraction portion" [within the "mixed fraction"] ; but instead of solving for the quotient—write in the format of a fraction:
In this case: " " .
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Now, substitute this "improper fraction" into our original problem; and rewrite:
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" " hours;
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We can reduce the "9" to "3" ; and the "6" to "2" ;
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{Since "9/6 = 3/2" };
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And rewrite as:
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" " hours ;
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Note: " \frac{31}{2} * \frac{3}{5} " ;
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= " " ;
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= 93 ÷ 10 ;
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= 9.3 hours.
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The answer is: " 9.3 hours " .
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Hope this explanation is helpful!
Best of luck to you in your academic pursuits!
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