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marusya05 [52]
3 years ago
6

Divide the number 20 into two parts (not necessarily integers) in a way that makes the product of one part with the square of th

e other as large as possible
use calculus methods
Mathematics
1 answer:
Ilya [14]3 years ago
3 0

Answer:

13 1/3 and  6 2/3.

Step-by-step explanation:

Let the 2 parts be x and (20 - x).

So x^2(20 - x) must be a maximum.

y = x^2(20 - x)

y = 20x^2 - x^3

Finding the derivative):

y' =  40x - 3x^2 = 0   for  maxm/minm value.

x( 40 - 3x) = 0

40 - 3x = 0

3x = 40

x = 40/3.

This is a maximum because the second derivative y" =  40 - 6x = 40 - 6(40/3)) is negative.

So the 2 numbers are 13 1/3 and  6 2/3.

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The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

<h3>Linear Function</h3>

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

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The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x  for finding the values of y.

Thus,

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       16*(-2)+4y=12

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      4y=12+32

     4y=44

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  • For x= -1,  the value of y will be:

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  • -16+4y=12
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  • 4y=28
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         16*(0)+4y=12

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         16*(1)+4y=12

  • 16+4y=12
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Read more about the linear equation here:

brainly.com/question/1884491

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7 0
2 years ago
Awnser and show your work &lt;3
marishachu [46]

Answer:

Team A: 25 players

Team B: 24 players

Step-by-step explanation:

Team A:

to find the total # of players of the team we need to set up a fraction. 5 out out of an unknown number of players is equal to 1/5, so we set it up as:

\frac{5}{x} = \frac{1}{5}

then we cross multiply to get

x*1 = 5*5

x=25 players

Team B

similarly to Team A

\frac{3}{x} = \frac{1}{8}

cross multiply to get

x*1=3*8

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