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
g100num [7]
3 years ago
11

The product of two numbers is 32. Find the sum of the two numbers S(x) as a function of one of the numbers, x. S(x) = Find the p

ositive numbers that minimize the sum and list them in increasing order: (smaller number) = ?(larger number) = ?Let c be the smaller of the two numbers that minimize the sum. Then c = ?S'(c) = ? and S"(c) = ?
Mathematics
1 answer:
Jobisdone [24]3 years ago
3 0

Answer:

c = 4\sqrt2\\\\S'(4\sqrt2) = 0\\\\S''(4\sqrt2)=\frac{1}{2\sqrt2}

Step-by-step explanation:

We are given the following information in the question:

The product of two numbers is 32.

Let the two numbers be x and y, then,

x\times y = 32\\\\y = \displaystyle\frac{32}{x}

The sum of the two numbers = S(x)

S(x) = x + \displaystyle\frac{32}{x}

First, we differentiate S(x) with respect to x, to get,

\displaystyle\frac{d(S(x))}{dx} = \frac{d( x +\frac{32}{x})}{dx} = 1 - \frac{32}{x^2}

Equating the first derivative to zero, we get,

\frac{d(S(x))}{dx} = 0\\\\1 - \frac{32}{x^2}= 0

Solving, we get,

x =\pm \sqrt{32}

Again differentiation S(x), with respect to x, we get,

\displaystyle\frac{d^2(S(x))}{dx^2} =\frac{64}{x^3}

Atx =\sqrt{32},

\frac{d^2(S(x))}{dx^2} > 0

Thus, minima occurs at x = \sqrt{32} for S(x).

If c be the smaller of the two numbers that minimize the sum, then,

c = \sqrt{32} = 4\sqrt2\\\\S'(c) = 1 - \displaystyle\frac{32}{32} = 0\\\\S''(c) = \frac{64}{32\sqrt{32}} = \frac{1}{2\sqrt2}

You might be interested in
Suppose that y varies inversely with x.Write an equation for the inverse variation Y=4 when x=7
myrzilka [38]

Answer:

If y varies inversely as x, then we write it as:

y = k/x


where k is some constant.


If we multiply both sides of this equation by x we get an equation for k:

k = x*y


We are given that y=4 when x=7, therefore:

k = 7*4 = 28


Put this back into our original equation to get:

y = 28/x



4 0
3 years ago
- 10 + 2y - 4<br> please help
Alecsey [184]

Answer:

2y+6

Step-by-step explanation:

2 negatives equal a positive

3 0
3 years ago
Divide.<br><br> 5892 ÷ 18<br><br><br> 327<br><br> 327118<br><br> 32713<br><br> 327718
kakasveta [241]
327 is gonna be your answer just use a calculator
6 0
3 years ago
Burj l Arab Hotel,one of the world's tallest buildings,was finished in 1999.Located in Dubai,it is 1,053 feet high with 60 stori
AlexFokin [52]

Each floor is 3.35 feet taller than each floor of the Aon Center


5 0
3 years ago
Mary has a pink dress, a blue dress, and a yellow dress. She has a black pair of shoes and a white pair. How many dress and shoe
Yanka [14]
There are two ways to solve this. 
The first way is logically. 
Mary can 
-wear a pink dress with black shoes   -wear a pink dress with white shoes
-wear a blue dress with black shoes   -wear a blue dress with white shoes
-wear a yellow dress with black shoes   - wear a yellow dress with white shoes

Count them up, and you'll get six combinations! 

Another way is simply mathematically, which is easier in my opinion. 

3 (different colored dresses) × 2 (different colored shoes) = 6 (combos)
8 0
3 years ago
Other questions:
  • A construction elevator can carry at most 2,320 pounds. If the elevator operator weighs 195 pounds and each palette of roofing m
    14·1 answer
  • What is the answer to (-6)-2-(-7) and solve it please
    9·1 answer
  • What is an equation for the line that passes through points (8.-3) and (9, 10)?
    12·1 answer
  • A boat costs $11850 and decreases in value by 10% per year how much will the boat be worth after 8 years
    8·2 answers
  • The points (6, -3) and (7, -10) fall on a particular line. What is its equation in point-slope form? Use one of the specified po
    12·1 answer
  • This is s free question so answer and get the points
    13·2 answers
  • There are 30 candies in a bag and you ate 9 of them what percentage did you eat?
    9·2 answers
  • What is pm ⋅ pn equal to?<br><br> pm − n<br> pm + n<br> pm ⋅ n<br> pm ÷ n
    8·1 answer
  • Simplify (a+3)-2(4+a)+5a_4<br>​
    12·1 answer
  • A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!