One non-negative number is the reciprocal of another number. The sum of the two numbers is a minimum. What are the two numbers

Answers

Answer 1

The two numbers are 1 and 1.

Let the non-negative number be x and its reciprocal be y = 1/x

The sum of the two numbers is f(x,y) = x + y

= x + 1/x

= f(x)

For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.

So, df(x)/dx = d(x + 1/x)/dx

= dx/dx + d(1/x)/dx

= 1 - 1/x²

Equating it to zero, we have

1 - 1/x² = 0

1 = 1/x²

x² = 1

Taking square-root of both sides, we have

x = ±√1

x = ±1

Since x is non-negative x = + 1

We differentiate f(x) again to determine if this value gives a minimum for f(x).

So, d²f(x)/dx² = d(1 - 1/x²)/dx

= d1/dx - d(1/x²)/dx

= 0 - × (-2/x³)

= 2/x³

Substituting x = 1 into the equation,

d²f(x)/dx² = 2/x³

= 2/1³

= 2 > 0.

So x = 1 is a minimum point for f(x)

Since x = 1 and y = 1/x, y = 1/1 = 1

So, the two numbers are 1 and 1.

Learn more about sum of two numbers here:

https://brainly.com/question/13854139


Related Questions

A rectangular poster has a area of 504 centimeters. The width of the poster is 14 centimeters. How long is the poster?

Answers

Answer:

36 cm

Step-by-step explanation:

504/14=36

You measure 43 randomly selected textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 12.4 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Answers

Answer:

by the empirical rule, 95% of the population is within 2 standard deviations of the mean

55 + or - 2(9.2) = 55+ or - 18.4 = (36.6,73.4)

95% of the population falls between 36.6 and 73.4 ounces

Step-by-step explanation:

fill in the missing value in each equation:
a)0.25+_____=0
b)-5×_____=-5
c)_____×-6=0

Answers

Answer:

a) -0.25

b) 1

c)0

Step-by-step explanation:

a) 0.25 + (-0.25)=0

b) -5*1=-5

c) 0*(-6)=0

The graph of the linear function is shown on the coordinate grid. What is the equation of this line?​

Answers

y=-1/3-2

Hope this helps!! :)

Please help me ASAP

Answers

Answer:

A: 9.5s+19.95 is less than or equal to 55

Step-by-step explanation:

She has no more than 55 dollars to spend so it cant be greater than but it can be equal to 55 so the answer is the first option

The primary difference(s) between the standard deviation and the coefficient of variation as measures of risk are:

Answers

How long does it have to be

Do y’all know the answer ….???

Answers

Answer:

$500

Step-by-step explanation:

John earns $100 per night.

He works 5 nights a week.

Therefore his weekly gross wage = $100 × 5

= $500

2. Solve the equation and check.
8x-8= 7 + 3x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answers

the answer is x=3 i believe

PLEASE IM GONNA DIE Paloma rides a scooter. She travels 10 ft. For every 1 second.

Hannah says that Paloma’s ratio of seconds traveled to feet traveled is 10:1. Is Hannah correct? Use a model to explain your thinking​

Answers

Answer:

She is incorrect; Paloma's ratio of seconds travelled to feet travelled is 1:10.

Step-by-step explanation:

Her ratio is 1:10 because the first number is the number of seconds, and the second number is the number of feet. So for every 1 second, she travels 10 feet, as indicated in the original problem.

Hope this helps.

Matthew Bailey, as manager of Designs by Bailey, is upgrading his CAD software. The high-performance (HP) software rents for $3,000 per month per workstation. The standard-performance (SP) software rents for $2,000 per month per workstation. The productivity figures that he has available suggest that the HP software is faster for his kind of design. Therefore, with the HP software he will need five engineers and with the SP software he will need six. This translates into a variable cost of $200 per drawing for the HP system and $240 per drawing for the SP system. At his projected volume of 80 drawings per month, which system should he rent?

Answers

Using linear functions, it is found that the high-performance system should be rented.

A linear function has the following format:

[tex]y = ax + b[/tex]

In which:

a is the slope, which is the variable cost.b is the y-intercept, which is the fixed cost.

With the high-performance software:

Fixed cost of $3,000 per month, hence [tex]b = 3000[/tex].Cost of $200 per drawing, hence [tex]a = 200[/tex]

Then, the model is:

[tex]C_{hp}(d) = 3000 + 200d[/tex]

With the standard-performance software:

Fixed cost of $2,000 per month, hence [tex]b = 2000[/tex].Cost of $240 per drawing, hence [tex]a = 240[/tex]

Then, the model is:

[tex]C_{sp}(d) = 2000 + 240d[/tex]

The costs for 80 drawings, that is, [tex]d = 80[/tex] for both cases are given by:

[tex]C_{hp}(80) = 3000 + 200(80) = 19000[/tex]

[tex]C_{sp}(80) = 2000 + 240(80) = 21200[/tex]

Due to the lower cost, the high-performance system should be rented.

A similar problem is given at https://brainly.com/question/20849340

Need help plz ! I'll give 30 points.​

Answers

Answer:

45 90 135 180 dkdhwjuwuhd

Ratios:
The number of Anna's baseball cards is 3/4 the number of Patricia's cards. If Anna gives half of her cards to Patricia, what will be the ratio of Anna's cards to Patricia's cards?

Answers

Answer:

3/11

Step-by-step explanation:

thank you for the poits

help plz we this work

Answers

Since it’s of 100, it’s how many squares are shaded in: 35
So it would be 35/100 or 35%
ANSWER: 35%

Please helpp for 17 points......
a. -4
b. -1
c. 1
d. 4

Answers

Answer: -4

Explanation: subtract 4 then 8 and so on

Answer:

Step-by-step explanation:

d

Help help help help help help

Answers

Answer:

Step-by-step explanation:

A' = (-1 + 4, 2 + 6) = (3, 8)

B' = (-2 + 4, -3 + 6) = (2, 3)

A' = (-5 + 4, -1 + 6) = (-1, 5)

geomtry plz help 15 points

Answers

Answer:

[tex]DE=5x-12[/tex]

Step-by-step explanation:

From this we can see this is an equilateral triangle

So, both sides to make every angle equal have to be the same

That's why [tex]DE=5x-12[/tex]

Brainliest please

Answer:

DE = 5x-12 (base angles of isos triangle)

Multiply or divide. write fractions in simplest form.

2/3 * (-2 1/4) * (-1 1/2)

i really need help with this problem! i will mark you brainliest :)

Answers

Step-by-step explanation:

Okay so, let's turn these into decimals first (rounded to nearest 2 thousandths).

2/3 = 0.66666 (repeating), to the nearest 2 thousandths would be 0.66.

-2 1/4 = -9/4 = -2.25

-1 1/2 = -3/2 = -1.5

then we set up the problem

0.66 × -2.25 × -1.5 = 2.2275 rounded 2.22 as an improper fraction 111/50 and that cannot be simplified any smaller.

What is the reciprocal of
5/6

Answers

Answer:

6/5

Step-by-step explanation:

need help with this i don't understand

Answers

Answer:

7see below5the rule is not one-to-one

Step-by-step explanation:

Applying the squaring rule to each of the elements of the domain, we get ...

  [tex]\begin{array}{cc}\text{Domain}&\text{Range}\\1&1\\-3&9\\-\frac{1}{2}&\frac{1}{4}\\3&9\\2&4\\\frac{1}{4}&\frac{1}{16}\\0.5&\frac{1}{4}\end{array}[/tex]

__

1. There are 7 different numbers in the Domain list.

2. See above

3. There are 5 different numbers in the Range list.

4. The rule "square me" is not "one-to-one" Two different values in the domain can result in the same value in the range. -3 and 3 both result in 9. -1/2 and 0.5 both result in 1/4.

HELP WITH GEOMETRY HOMEWORK ASAP!!!

Answers

Answer:

26°

Step-by-step explanation:

90°+64°+x°=180° (Sum of all the angles in a right angled triangle=180°)

154°+x°=180°

x°=180-154°

x°=26°

15. A farmer records the number of eggs that chickens on the farm produce each week. The table
shows the results.
143
160
117
137
152
108
128
If during the next week, the chickens on the farm produce 60 eggs, which statement is true?
A The value 60 is an outlier that will skew the data to the left.
B The value 60 is an outlier that will skew the data to the right.
С The value 60 is not an outlier, and it will not skew the data in either direction.
D
The value 60 is not an outlier, and the effect on the data is unknown.

Answers

The answer to the question you are asking is 56

what is the first three elements of an arithmetic sequence are -13 , -8 and -3, which elements is 182?

Answers

An arithmetic sequence is a sequence where the difference d between successive terms is constant. The general term of an arithmetic sequence can be written in terms of its first term a1, common difference d, and index n as follows: an=a1+(n−1)d.

Given h(t) = -2(t+ 5)^2 +4, find h(-8).

Answers

Answer:

Substitute -8 as x into the equation.

h(-8)=-2(-8+5)^2+4

h(-8)=-2(-3)^2+4

h(-8)=-2(9)+4

h(-8)=-18+4

h(-8)=-14

:)

75 is what percent of 150

Answers

Question:

75 is what percent of 150

Explanation:

Percentage Calculator:75 is what percent of 150=50

Answer:

50

Answer:

75 is 50 percent of 150.

Step-by-step explanation:

This is a pretty simple concept. First of all for this question, you should have noticed that 75 is half of 150. 50% is equal to 1/2.

There are a couple of methods you could use to solve this problem, if you are using a calculator, a simple way to solve percentage problems is to do 75 divided by 150 (in this case) which gives you 0.50.

If you do not have a calculator and you have to do this on paper, you need to do the classic proportion method. Make two fractions, 75 over 150, and x over 100. (x is what is used to represent an unkown amount.)

We are using over 100 because that is what a percent represents: an amount that is a fraction of 100. now you need to cross multiply. That would be 75 x 100. That equals 7,500. Now cross multiply the other way. That is 150x or represent 150 times x. Now solve the equation 150x = 7,500. To solve this you need to isolate the variable, x by dividing the 150 multiplying the x. That is the coefficient. the attached number next to it. After you do that, you need to divided the other side of the equation by 150. 7,500 divided by 150 equals 50.

After that you will find that the equation shows the value x = 50. You have now found the value of x.

I hope this helps :)

I need answers to all of these and explanation as well. Thank you.

Answers

4) d

let's firstly convert the mixed fractions to improper fractions, and then proceed

[tex]\stackrel{mixed}{4\frac{3}{8}}\implies \cfrac{4\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{35}{8}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ -4\frac{3}{8}-\left( -1\frac{1}{4} \right)\implies -\cfrac{35}{8}-\left( -\cfrac{5}{4} \right)\implies -\cfrac{35}{8}+\cfrac{5}{4}\implies \cfrac{-(1)(35)~~ +~~(2)(5)}{\underset{\textit{using this as LCD}}{8}}[/tex]

[tex]\cfrac{-35+10}{8}\implies -\cfrac{25}{8}\implies -3\frac{1}{8}[/tex]

5)

hmmm we can pick any of those %, hmmm let's use 18%, keeping in mind that the whole amount is really the 100% and that's say "x", hmmm we know the 18% of "x" is $5.87.

[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 18&5.87\\ 100&x \end{array}\implies \cfrac{18}{100}=\cfrac{5.87}{x}\implies \cfrac{9}{50}=\cfrac{5.87}{x} \\\\\\ 9x = 293.5\implies x = \cfrac{293.5}{9}\implies x = 32.6\overline{1}\qquad \textit{about 32 bucks and 61 cents}[/tex]

PLEASE HELP WILL MARK BRAINEST
If I || m, find the values of x and y.

Answers

Look at the photo.........................

Answer:

x = 8, y = 89/9

Step-by-step explanation:

Because of parallel lines, some angles are the same, see the attached image. That also means that (12x-28) + (9y-77) = 180 because they are half of an angle. So:

(12x-28) + (9y-77) = 180 ->

12x + 9y = 185.

Then,

(7x+12) = (12x-28) ->

x = 8.

We can plug that into the last equation:

12(8) + 9y = 185 ->

y = 89/9

:)

what is the perimeter of khgj?

Answers

Answer:

  58 in

Step-by-step explanation:

The fact that the rectangles are congruent means both have a length of 18 in and a width of 11 in. The perimeter is ...

  P = 2(L +W)

  P = 2(18 in + 11 in) = 2(29 in)

  P = 58 in

The perimeter of KHGJ is 58 inches.

What is the value of the expression 3 (5to the 3rd power) + 4t to the 2nd power when s = 5 and t = 3?

Answers

Answer:

  411

Step-by-step explanation:

Put the values where the variables are and do the arithmetic.

  3s³ +4t² = 3(5³) +4(3²)

  = 3(125) +4(9) = 375 +36 = 411

.45 is 1/10 of what?

Answers

Answer:

The answer is 4.5

When asked to factor the trinomial 8x^2-8x-16) a student gives the answer (X - 2)(x + 1). What is one thing wrong with this answer? - A. 8 is also a factor of this trinomial B. The minus sign should be a plus sign C. The factors are not simplified D. There is nothing wrong with the answer​

Answers

Answer:

8 is also a factor of this trinomial

Step-by-step explanation:

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