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
omeli [17]
3 years ago
6

Find two positive numbers satisfying the given requirements. The product is 432 and the sum of the first plus three times the se

cond is a minimum.
Mathematics
1 answer:
kogti [31]3 years ago
4 0

Answer:

<h3>36 and 12</h3>

Step-by-step explanation:

Let the two positive integers be x and y.

If their product is 432, then

xy = 432 ......... 1

Also if the sum of the first plus three times the second is a minimum, then;

p(x) = x + 3y

From 1;

y = 432/x ..... 3

Substitute 3 into 2;

p(x) = x+3y

p(x)= x + 3(432/x)

p(x) = x + 1296/x

Since the expression is at minimum when dp(x)/dx = 0

dp/dx = 1 + (-1296)/x²

dp/dx = 1  -1296/x²

0 =  1  -1296/x²

0 = (x²-1296)/x²

cross multiply

0 = x²-1296

x² = 1296

x = √1296

x = 36

Since xy = 432

36y = 432

y = 432/36

y = 12

Hence the two positive numbers are 36 and 12

You might be interested in
Which function has an axis of x=-2
coldgirl [10]

Give me the whole question including information, and graphs.

8 0
3 years ago
A truck driver is going down a one way street the wrong way, and passes at least ten cops. Why is he not caught?
Murljashka [212]
The truck driver was walking
4 0
3 years ago
How do I pick what subject I'm trying to get an answer for<br>​
Lyrx [107]
Top left corner probably depends on what device you’re using
6 0
3 years ago
Read 2 more answers
Simplify <br><img src="https://tex.z-dn.net/?f=5%20%7B%20%7D%5E%7B2%7D%20%20-%204%20%7B%7D%5E%7B2%7D%20%20%3D%20" id="TexFormula
garri49 [273]
5 · 5 - 4 · 4 = 9 sorry if I'm wrong
the dots mean to multiply
5 0
3 years ago
(3ab+2c)^3 what is the answer
svet-max [94.6K]

Answer:

=27a^3b^3+54a^2b^2c+36abc^2+8c^3

Step-by-step explanation:

(3ab+2c)^3

=(3ab+2c) × (3ab+2c) ×

=(3ab+2c)(9a^2b^2+12abc+4c^2)

=(3ab)(9a^2b^2)+(3ab)(12abc)+(3ab)(4c^2)+(2c)(9a^2b^2)+(2c)(12abc)+(2c)(4c^2)

=27a^3b^3+36a^2b^2c+12abc^2+18a^2b^2c+24abc^2+8c^3

=27a^3b^3+54a^2b^2c+36abc^2+8c^3

<em>hope this helps....</em>

5 0
2 years ago
Other questions:
  • I need help on this problem. Please help me.
    5·2 answers
  • In a sample of 60 diners at a restaurant, 12 had ordered an appetizer. If the restaurant serves 800 diners each day, how many ar
    6·2 answers
  • A team of bakers can roll and form 5 dozen pretzels in 9 minutes. How many pretzels can this team form in 1 hour?
    6·1 answer
  • If f(x) = 2x +4, which of the following is the inverse of f(x)?
    11·1 answer
  • Logan told a joke to 3 of his friends. Each of his friends told the joke to 3 more friends who each told the joke to 3 friends.
    11·2 answers
  • The unit rate is .4 right
    13·2 answers
  • A ___ of linear equations is a set of two or more linear equations that are dealt with together at the same time and involve the
    15·2 answers
  • Question 6 (1 point)
    6·1 answer
  • Jorge was studying average life expectancy in Europe and how it varies across different countries. He wanted to discover what va
    6·1 answer
  • Select all of the solutions to the following inequality. 4x+6 &gt; 3x-9
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!