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olchik [2.2K]
3 years ago
7

Please help me with this AP Calculus question!!

Mathematics
1 answer:
Temka [501]3 years ago
7 0

9514 1404 393

Answer:

  B.  3

Step-by-step explanation:

If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.

  dy/dx = 3 at x = 4

__

The derivative of the expression can be found from the quotient formula:

  d(u/v) = (du·v -u·dv)/v²

  y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2

  = (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2

  = (x^2 -4x +12)/(x -2)^2

  = ((x -4)x +12)/(x -2)^2

Then for x=4, we have ...

  y' = 12/4 = 3

  dy/dx = 3 at x = 4

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100 notes were altogether

<em><u>Solution:</u></em>

Given that ratio of the number of $2 notes to the number of $5 notes was 4 : 1

number of $2 notes : number of $5 notes = 4 : 1

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Let 1x be the number of $ 5 notes

Given that total value of notes is $ 260

Therefore,

$ 2 (number of $ 2 notes ) + $ 5(number of $ 5 notes ) = $ 260

$ 2(4x) + $ 5(1x) = $ 260

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x = 20

<em><u>Thus number of notes altogether is given as:</u></em>

4x + 1x = 4(20) + 1(20) = 80 + 20 = 100

Thus 100 notes were altogether

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