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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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I'm not smart and I stink at math so can someone plz help me 12/x = 8
tensa zangetsu [6.8K]

1. We need to get rid of all the denominator in this equation.

  • This can be done by multiplying left and right sides by the LCD.
  • In the problem: 12/x = 8, the LCD is X.

12/x = 8 is now 12 = x * 8

1a. 8 * x = 8x

Now, your answer is 3/2, but It's improper. Let's convert it into a mixed number.

Subtract 3 by 2.

3 - 2 = 1

3/2 = 1 1/2

Therefore, your answer is 1 1/2. Also, the answer is 1.5.

4 0
3 years ago
What is the inverse of the function H(x)=3/4x+12
Mrac [35]

Answer:

h^{-1}(x) = \frac{4x-48}{3}

Step-by-step explanation:

let y = h(x) and rearrange making x the subject, that is

y = \frac{3}{4} x + 12 ( multiply through by 4 to clear the fraction )

4y = 3x + 48 ( subtract 48 from both sides )

4y - 48 = 3x ( divide both sides by 3 )

\frac{4y-48}{3} = x

Change y back into terms of x, thus

h^{-1} (x) = \frac{4x-48}{3}

3 0
4 years ago
-4.41666666667 as fraction help
blagie [28]

Answer:

-53/12

Step-by-step explanation:

4 0
3 years ago
A microchip manufacturer has determined that 6% of the processors they produce are defective. A quality technician performs the
Alborosie

Answer:

The expected value for the number of inspections until a defective unit is found 17.

Step-by-step explanation:

Percentage of defective microchips = 6%

Let the total number of inspection = x

number of defective microchip = 1

As we know

1/x = 6%

1/x = 0.06

x = 1/ 0.06

x = 16.67 inspections

x = 17 ( rounded off to nearest whole number )

17 inspection is done until the defective microchip is found.

3 0
4 years ago
Plsss help meee!!!!!!​
Lina20 [59]

Answer:

  • given below

Step-by-step explanation:

1)

total area = rectangle area + 2 triangle area

                =  length * width = 2 ( \frac{1}{2} * base * height )

                =  7.5 * 6 + 2 (  \frac{1}{2} * 3 * 4 )

                = 57 ft²

2)

separate it into two rectangles:

length * width + length * width

  6  *   2  +  9 * 4

      48 cm²

3)

parallelogram area =  base * height

                                = 20 * 25

                                 = 500 in²

6 0
3 years ago
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