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nasty-shy [4]
3 years ago
11

If p(x) = 3+4x-4x^2 represents the profits in selling x thousand boombotix speakers, how many speakers should be sold to maximiz

e profits?
Mathematics
1 answer:
Harman [31]3 years ago
4 0

Hello from MrBillDoesMath!

Answer:   500

Discussion:

The idea is to represent p(x)  with a squared component...

3 + 4x - 4x^2 =

3  - ( 4x^2 - 4x) =                  

Add and subtract 1:

(3+1) - (4x^2-4x +1) =

4 - (2x-1)^2


To maximize profit we need to minimize the term (2x-1)^2  as it is always positive (or zero) and subtracts from the number 4.  The minimum of (2x -1)^2 occurs when 2x -1 = 0 or x = 1/2. Since x is the number of speakers in thousands, (1/2)x = 500 speakers.

Note: this problem can be more easily addressed in a Calculus course by taking the first derivative of p(x), setting it to zero, and solving for x (which yields x = 1/2 too)




Thank you,

MrB

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To divide powers of the same base, we place the same base and subtract the exponents:

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-5/12-(-9/3) Reduce to simplest form
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Answer:

2 7/12

Step-by-step explanation:

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The equivalent equation is

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LCD(-5/12, 9/3) = 12

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

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Complete the multiplication and the equation becomes

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−5+36/12=31/12

This fraction cannot be reduced.

The fraction

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Convert to a mixed number using

long division for 31 ÷ 12 = 2R7, so

31/12=2 7/12

Therefore:

−5/12−−9/3=2 7/12

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hope it helps, kaul

thanks

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