1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marusya05 [52]
2 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]2 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.

You might be interested in
Find the theoretical probability of rolling a number cube labeled 1-12 and<br> it landing on 7.
Rashid [163]

Answer:

1/12

Step-by-step explanation:

There are 12 sides, and 7 is one of them. Therefore, there is a 1/12 chance of it landing on that side if it is a fair cube.

3 0
3 years ago
ANSWER FAST PLZ 25 POINTS!!!!!!!!!!!!!!!!!
Cloud [144]

Answer:

d

Step-by-step explanation:

hope it helps

3 0
2 years ago
At a store each notebook has a cost of X dollars. which situation can be represented by this inequality​
nadezda [96]

Answer:

a

the cot of 5 notebook is greater than the cost of 3notebooks plus a $2 pen

7 0
3 years ago
Help me plz someoneee
Charra [1.4K]

Answer:

Step-by-step explanation:

5 0
3 years ago
Use the product property of roots to choose the expression equivalent to 3√5x*3√25x^2?
nignag [31]

Answer: \sqrt[3]{125x^3}.


Step-by-step explanation: Given radical expression

\sqrt[3]{5x} \times \sqrt[3]{25x^2}.

According to the product property of roots.

\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a \times b}

On applying above rule, we get

\sqrt[3]{5x} \times \sqrt[3]{25x^2} = \sqrt[3]{5x \times 25x^2}

5 × 25 = 125 and

x \times x^2 = x^3

Therefore,

\sqrt[3]{5x \times 25x^2}= \sqrt[3]{125x^3}

<h3>So, the correct option would be second option \sqrt[3]{125x^3}.</h3>

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which ordered pair is a solution of the equation? − 7 x + 3 y = 2 −7x+3y=2
    9·1 answer
  • What does the line y=k-1/4a represent in y=a(x-h)^2+k, the standard form of equation for a parabola?
    6·2 answers
  • -2 X-9=3. Please help<br> 3
    5·2 answers
  • Mrs . Porcelli’s classroom bulletin board is 2/1/4 feet long. Ms .Smith bulletin board is 3 times as long Mrs . Porcelli’s.How l
    8·1 answer
  • The following questions are adding and subtracting polynomials
    9·1 answer
  • 3 = -3 + -2v<br> = 1<br> What is this
    9·1 answer
  • a game consists of placing seeds in 24 cups. a player puts two seeds in the first cup, four in the second, six in the third and
    6·1 answer
  • Mariel wrote these checks from her checking account: $10, $10, $31, and $10. Which number shows the change of balance in her che
    12·2 answers
  • What would x need to be in order to ensure that line k is ll to line m?
    11·1 answer
  • Show all three ways to write the ratio.<br><br> For every 12 shirts, I have 18 pants.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!