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.

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Related Questions

What is the meaning of the point shown on this graph?
Mysha’s Height

A: Mysha was 12 inches tall at age 2 1/2 years

B. Mysha was 30 inches tall at age 1 year

C: Mysha was 12 inches tall at the ago 30 months

D: Mysha was 30 inches tall at age 12 years

Answers

It would be B. She is 30 inches in height (y-axis) and she is 1 year old, or 12 months (x-axis). Hope this helped :)

Jane Rose’s semimonthly salary is $750. Her yearly salary is A.$9000 B. $12,500 C. $18,000 D. $19,500 E. $21,000

Answers

A because 750 times 12 because there is 12 months in a year. You get 9000

Answer:

C. $18,000

Step-by-step explanation:

Given that her semimonthly salary is $750, find her yearly salary.

Semimonthly means twice a month, meaning that she will receive 24 paychecks every year.

750x24=18,000

=$18,000

Hope this helps :)

What is slope I need help finding the slope please help me

Answers

The slope is 3 this is intergers solution the right side is positive and left side is negative

A shipment contains 10 igneous, 8 sedimentary, and 8 metamorphic rocks If 8 rocks are selected at random, find the probability that exactly 6 are sedimentary
The probability that exactly 6 of the rocks are sedimentary is
(Round to four decimal places as needed.)

Answers

The probability that exactly 6 are sedimentary is 0.00002

Probability is the likelihood or chance that an event will occur.

Given the total amount of rocks = 10 + 8 + 8 = 26 rocks

If there is a total of 8 sedimentary rocks, the total outcome will be expressed as:

26C8 = 26!/(26-8)!8!

26C8 = 1562275

If exactly 6 are sedimentary are selected out of 8 sedimentary rocks, then the expected outcome is ;

8C6 = 8!/(8-6)!6!

8C6 = 28

Pr(exactly 6 are sedimentary ) = 28/1562275

Pr(exactly 6 are sedimentary ) = 0.000017922

Hence the probability that exactly 6 are sedimentary is 0.00002

Learn more on probability here: https://brainly.com/question/13604758

Drag the tiles to the correct boxes. Not all tiles will be used. What are the domain and the range of function f? range arrowRight domain arrowRight

Answers

the domain is the first one and the 2nd one (going down) is the range

here are the correct answers :)

Need some help with these 2 math questions, They are related so best to finish one then work on the bisect. Thank you.

Answers

Answer:

∠RQT = 23.5

∠PQR  = 133°

Step-by-step explanation:

Question 1

Step 1 - Add angles together:

As all angles on a straight line must add up to 180°:

3x - 5 + x + 1 = 180

Add like terms together

3x + x - 5 + 1

4x - 4 = 180

Step 2 - Add 4 to both sides of the equation:

4x - 4 + 4 = 180 + 4

4x = 184

Step 3 - Divide both sides by 4:

[tex]\frac{4x}{4} = \frac{184}{4}[/tex]

x = 46

∠RQS = x + 1

∠RQS = 46 + 1

∠RQS = 47

Given the ray QT bisects ∠RQS, the angles must be the same on either side so:

47 ÷ 2 = ∠RQT

∠RQT = 23.5

Question 2

As we know the value of x:

∠PQR = 3x - 5

Plug known values in:

3x - 5

3(46) - 5

138 - 5

∠PQR  = 133°

This can also be calculated by subtracting known angle ∠RQS from 180:

180 - 47 = 133.

Hope this helps!

Based on a​ poll, 63% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot. What is the probability that among four randomly selected Internet​ users, at least one is more careful about personal information when using a public​ Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to​ respond? The probability that at least one of them is careful about personal information is

Answers

Answer:

So it's a big probability it's a 6 in 4 chance though. 6 is for users that are careful and 4 for users that aren't that careful.

Step-by-step explanation:

The required probability is 0.981 that at least one of them is careful about personal information.

What is the Binomial Theorem?

The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.

According to a survey, 63% of Internet users are more cautious about their personal information when using a public Wi-Fi hotspot.

Four randomly selected Internet​ users, at least one is more careful about their personal information.

As per the given question,

Here, n = 4, p = 0.63, (1 - p) = 0.37 and x = 0

As per binomial distribution formula P(X = x) = nCx × p^x × (1 - p)^(n - x)

P(X = 0) = 4C0 × 0.63^0 × 0.37^4

P(X = 0) = 0.0187

P(X ≥ 1) = 1 - 0.0187

Apply the subtraction operation, and we get

P(X ≥ 1) = 0.981

Thus, the required probability is 0.981 that at least one of them is careful about personal information.

Learn more about the binomial theorem here:

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The perimeter of the smallest square is 48 feet. What is the perimeter of the largest square?

Answers

Answer:

x > 48

Step-by-step explanation:

There’s nothing told to us or showed to us to answer It So I was only able to answer it with an inequality :(((

sorry if this didn’t help but once again… not enough information :(

math
(5 points) will mark brainliest!! pls help :)

Answers

(tv^3)/(u^8) (you can get the answer by cancelling out the same variables in the numerator and denominator

Answer:  [tex]\frac{tv^3}{u^8}\\\\\\[/tex]

This is the fraction tv^3 all over u^8

=========================================================

Work Shown:

[tex]\frac{t^2uv^7}{tu^9v^4}\\\\\\\frac{t^2}{t}*\frac{u}{u^9}*\frac{v^7}{v^4}\\\\\\t^{2-1}*u^{1-9}*v^{7-4}\\\\\\t^{1}*u^{-8}*v^{3}\\\\\\\frac{t}{1}*\frac{1}{u^8}*\frac{v^3}{1}\\\\\\\frac{t*1*v^3}{1*u^8*1}\\\\\\\frac{tv^3}{u^8}\\\\\\[/tex]

In the third step, I used the rule (a^b)/(a^c) = a^(b-c)

To make the negative exponent turn positive, we apply the reciprocal to the base.

11/6= 1/p



Pls help!!

Answers

Answer:

p = 6/11

Step-by-step explanation:

11/6 = 1/p

=> 11p = 6

=> p = 6/11

Hoped this helped.

If 2x + y = 7, what is the value of y when x = 3? A. 1 B. 3 C. 5 D. 7 E. 9

Answers

Answer:

the correct answer is A.1

the result is explained below in the photo

Answer:

y = 1

Step-by-step explanation:

2x + y = 7

x = 3

plug in 3 for x

2(3) + y = 7

Multiply 2 * 3

6 + y = 7

Therefor y = 1

Pre college need help

Answers

Answer:

sorry I can't answer that because I need points very3× sorry

find the velue of y? y²=169​

Answers

Answer:

-13 or 13

Step-by-step explanation:

Since we are looking for the square root of 169, we realize that 13 multiplied by itself equals 169. Negative 13 does the same, so it is the answer.

What would the answer be

Answers

Answer:

B.

Step-by-step explanation:

process of elimination. the red dot is not a 1/4 of the number of lines, so it cant be 12.25, 13.625 is impossible because it has a value less than 13, and 12.625 is impossible as well because it has a value less than 12.5 therefore 12.375 is the best answer, and the only correct answer

geomtry plzz help 15 points

Answers

Answer:

False.

Step-by-step explanation:

The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side. However, 8+6=14 is less than 15. Hence, the triangle cannot be formed.

What expression is equivalent to 5(x+7)

Answers

Answer:

5x + 35

Step-by-step explanation:

Which of the following is NOT true about the expression?
-5x3 + 12x2 - 9x - 8
It has a leading term of 5
O The leading coefficient is 5,
The constant term is 8.
ch
O There are no negative coefficients

Answers

The statements which is not true about the expression given is; It has a leading term of 5.

According to the question;

The expression given is; -5x3 + 12x2 - 9x - 8.

Since it is an expression; all other statements can be assumed true except; It has a leading term of 5; in which case the leading term is; -5x³

As such, the statements which are not true is;

It has a leading term of 5

Read more:

https://brainly.com/question/11386252

Will the answer to the subtraction problem below be odd or even?
5291 - 4070 = ?

Answers

Answer:

1221

Step-by-step explanation:

here you go ...........

even because the answer is 1221

Write a polynomial function with given zeros √8, √10

Answers

Answer:

y = x^2 - (sqrt(8) + sqrt(10))x + sqrt(80)

Step-by-step explanation:

we do y = (x- sqrt8)(x -sqrt10) and simplify

Rationalize the denominator.

9-10/2
V2+1

Answers

Answer:

  d.  19√2 -29

Step-by-step explanation:

Multiply numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{9-10\sqrt{2}}{\sqrt{2}+1}=\dfrac{(9-10\sqrt{2})(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}\\\\=\dfrac{9\sqrt{2}-9-10\cdot2+10\sqrt{2}}{2-1}=\boxed{19\sqrt{2}-29}[/tex]

Answer:

Step-by-step explanation:

jelp pls with 2 work pps brainly ​

Answers

Answer:

The underline one is 40.

Missing numbers. 35, 40 45, 50, 55, 60, 65, 70.

Step-by-step explanation:

Add 5 rule

Answer:

5. The tens place.

6. 35, 40, 45, 50, 55, 60, 65.... (And so on)

Step-by-step explanation:

Hoped this helped.

According to this diagram, what is sin 23°?
67°
13
5
Сл
23°
90°
12
O A.
13
5
12
O B.
B. 13
12
13
O c.
c.13
O D.
D.
5
13
O E.
13
12
5
OF.

Answers

Using relations in a right triangle, it is found that the sine of 23 degrees is given by:

D. 5/13.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

Looking at the graph, the side opposite to the angle of 23º is of 5, while the hypotenuse is of 13, hence the sine is given by:

sin(23º) = 5/13.

Which means that option D is correct.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

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will give 25 points if right

Answers

The slope of the equation is 1/6

Answer:

1/6

Step-by-step explanation:

When the equation is in the form "y = mx + b", m is the slope. This linear line has a slope of 1/6 and a y-intercept of -1/2.

Hey help please math I need help good luck I’ll I’ve point

Answers

Answer:

180 degrees

Step-by-step explanation:

180 degrees would flip the triangle halfway through a full circle. B is A upside down rotated halfway through a full circle.

What is the equation (y=mx+b) for the points (3,-1) and (4,7) PLZ SHOW HOW YOU GOT THE Y-INTERCEPT

Answers

Answer:

[tex]y=8x-25[/tex]

Step-by-step explanation:

The first thing to do is to find the slope. The slope is the difference in Y divided by the difference in x, or:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here (3, -1) is going to be (x1, y1) and (4, 7) will be (x2, y2):

[tex]m=\frac{7--1}{4-3}=\frac{8}{1}=8[/tex]

The slope is 8. Now, you can plug that into the formula. To find the y-intercept, plug in any point on the line and solve for b:

[tex]y=mx+b\\-1=8(3)+b\\-1=24+b\\b=-25[/tex]

Now we have both the slope and the y-intercept so you can write the equation for the line:

[tex]y=8x-25[/tex]

You can test that either by checking y for some value of x, or by graphing.

A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?

Enter the correct answer in the box.

Answers

Answer:

The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL

Step-by-step explanation:

12 inches = 1 foot

Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram

So for length:

10:(15*12)

10:180

1:18

And for width:

8:12(12)

8:144

1:18

Answer:

18 inches

Step-by-step explanation:

The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.

1 foot= 12in x 1ft= 12 inches

15 feet= 12in x 15ft = 180 inches

12 feet= 12in x 12ft = 144 inches

The room is 180 inches long and 144 inches wide.

To find the scale, set up a proportion to the drawing to the room.

[tex]\frac{10}{8} =\frac{180}{144}[/tex]

You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.

Factor this completely thank you

Answers

4(2x raise to power 2-4-7x)

13. Tell whether the sequence is arithmetic. If it is, what is the common difference? (1 point)
-5.-2,2,7..

A. yes: 3
B. yes: 4
C. yes: 3
D. no

Answers

Answer:

I think the answer is c

On average, Laylah drinks 1/2 of a 6-ounce glass of water in 2/3 hour. What is 1/2 of 6?

Answers

Answer:3

Step-by-step explanation:

1/2 of 6 is 3 because (6x1)/2=6/2 which equals 3

Which associations best describe the scatter plot?

Select each correct answer.


Linear association

Negative association

Positive association

Nonlinear association

Answers

Linear = straight line or constant slope
But in this case, it’s more exponential
Negative: start high - goes lower
Positive: start lower - goes higher

Solution: non-linear and negative
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